Cremona's table of elliptic curves

1975 = 5² · 79

Field	Data	Notes
Atkin-Lehner	5+ 79+	Signs for the Atkin-Lehner involutions
Class	1975a	Isogeny class
Conductor	1975	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3042975078125 = 57 · 794	Discriminant
Eigenvalues	1  0 5+  4  4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3917,44116]	[a1,a2,a3,a4,a6]
Generators	[84:508:1]	Generators of the group modulo torsion
j	425428681761/194750405	j-invariant
L	3.7657887801095	L(r)(E,1)/r!
Ω	0.71708303689442	Real period
R	2.625768973994	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	31600l3 126400b3 17775w4 395a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1975a3

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	+	4	4	-6	-6	-4	0	6	0	-10	2	-8	-12	14	-4	-10	4	-8	-2	+	-4	-6	-10

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Quadratic twists for elliptic curve 1975a3

-4	8	-3	5	-7
31600l3	126400b3	17775w4	395a3	96775d3

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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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