Cremona's table of elliptic curves

1961 = 37 · 53

Field	Data	Notes
Atkin-Lehner	37- 53-	Signs for the Atkin-Lehner involutions
Class	1961a	Isogeny class
Conductor	1961	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3845521 = 372 · 532	Discriminant
Eigenvalues	1  0  2  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-46,87]	[a1,a2,a3,a4,a6]
Generators	[-2410:14603:1000]	Generators of the group modulo torsion
j	10896752313/3845521	j-invariant
L	3.8498329894203	L(r)(E,1)/r!
Ω	2.277538633284	Real period
R	6.7613922032475	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	31376c2 125504a2 17649c2 49025a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1961a2

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
1	0	2	0	4	-2	-6	-4	0	-2	0	-	-6	4	-8	-	12	-6	-8	12	-6	-8	-16	-14	10

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Quadratic twists for elliptic curve 1961a2

-4	8	-3	5	-7	37	53
31376c2	125504a2	17649c2	49025a2	96089a2	72557d2	103933c2

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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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