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
Δ	-777362416259 = -1 · 115 · 136	Discriminant
Eigenvalues	2 -1 -1  2 11+ 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1746,-50295]	[a1,a2,a3,a4,a6]
Generators	[42270:573985:216]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	4.5229958287478	L(r)(E,1)/r!
Ω	0.35201532506738	Real period
R	6.4244302828039	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	29744z2 118976bb2 16731m2 46475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1859a2

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 1859a2

-4	8	-3	5	-7	-11	13
29744z2	118976bb2	16731m2	46475a2	91091f2	20449g2	11a1

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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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