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	2437890625 = 58 · 792	Discriminant
Eigenvalues	1  0 5+  4  4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3292,73491]	[a1,a2,a3,a4,a6]
Generators	[4596:26577:64]	Generators of the group modulo torsion
j	252555814161/156025	j-invariant
L	3.7657887801095	L(r)(E,1)/r!
Ω	1.4341660737888	Real period
R	5.2515379479879	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	31600l2 126400b2 17775w2 395a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1975a2

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 1975a2

-4	8	-3	5	-7
31600l2	126400b2	17775w2	395a2	96775d2

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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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