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	1	Product of Tamagawa factors cp
deg	114	Modular degree for the optimal curve
Δ	1961 = 37 · 53	Discriminant
Eigenvalues	1  0  2  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-41,112]	[a1,a2,a3,a4,a6]
Generators	[-18:119:8]	Generators of the group modulo torsion
j	7727161833/1961	j-invariant
L	3.8498329894203	L(r)(E,1)/r!
Ω	4.5550772665679	Real period
R	3.3806961016237	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31376c1 125504a1 17649c1 49025a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1961a1

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 1961a1

-4	8	-3	5	-7	37	53
31376c1	125504a1	17649c1	49025a1	96089a1	72557d1	103933c1

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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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