Cremona's table of elliptic curves

275 = 5² · 11

Field	Data	Notes
Atkin-Lehner	5+ 11-	Signs for the Atkin-Lehner involutions
Class	275b	Isogeny class
Conductor	275	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	-171875 = -1 · 56 · 11	Discriminant
Eigenvalues	2  1 5+  2 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-8,19]	[a1,a2,a3,a4,a6]
j	-4096/11	j-invariant
L	2.8380382820443	L(r)(E,1)/r!
Ω	2.8380382820443	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4400m1 17600e1 2475h1 11a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 275b1

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	+	2	-	-4	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 275b1

-4	8	-3	5	-7	-11	13	17	-19
4400m1	17600e1	2475h1	11a3	13475j1	3025g1	46475a1	79475e1	99275e1

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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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