Cremona's table of elliptic curves

1859 = 11 · 13²

Field	Data	Notes
Atkin-Lehner	11+ 13+	Signs for the Atkin-Lehner involutions
Class	1859a	Isogeny class
Conductor	1859	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-53094899 = -1 · 11 · 136	Discriminant
Eigenvalues	2 -1 -1  2 11+ 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-56,405]	[a1,a2,a3,a4,a6]
Generators	[-6:165:8]	Generators of the group modulo torsion
j	-4096/11	j-invariant
L	4.5229958287478	L(r)(E,1)/r!
Ω	1.7600766253369	Real period
R	1.2848860565608	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29744z1 118976bb1 16731m1 46475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1859a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
2	-1	-1	2	+	+	-2	0	-1	0	-7	-3	8	-6	-8	-6	-5	12	7	3	-4	-10	6	-15	7

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Quadratic twists for elliptic curve 1859a1

-4	8	-3	5	-7	-11	13
29744z1	118976bb1	16731m1	46475a1	91091f1	20449g1	11a3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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