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	-291947797 = -1 · 37 · 534	Discriminant
Eigenvalues	1  0  2  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,139,494]	[a1,a2,a3,a4,a6]
Generators	[55380990:332448383:9261000]	Generators of the group modulo torsion
j	295807676247/291947797	j-invariant
L	3.8498329894203	L(r)(E,1)/r!
Ω	1.138769316642	Real period
R	13.522784406495	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	31376c3 125504a3 17649c4 49025a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1961a4

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 1961a4

-4	8	-3	5	-7	37	53
31376c3	125504a3	17649c4	49025a3	96089a3	72557d3	103933c3

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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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