Cremona's table of elliptic curves

2257 = 37 · 61

Field	Data	Notes
Atkin-Lehner	37- 61+	Signs for the Atkin-Lehner involutions
Class	2257a	Isogeny class
Conductor	2257	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	137677 = 37 · 612	Discriminant
Eigenvalues	0  1 -4 -3 -3 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-15,-20]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1] [10:30:1]	Generators of the group modulo torsion
j	398688256/137677	j-invariant
L	2.9488660934858	L(r)(E,1)/r!
Ω	2.4806043108045	Real period
R	0.594384618426	Regulator
r	2	Rank of the group of rational points
S	0.99999999999963	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36112h1 20313f1 56425a1 110593f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2257a1

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
0	1	-4	-3	-3	-4	-2	-4	0	-6	-4	-	3	-2	7	-5	-10	+	-4	15	-9	4	-3	-8	-6

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Quadratic twists for elliptic curve 2257a1

-4	-3	5	-7	37
36112h1	20313f1	56425a1	110593f1	83509a1

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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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