Cremona's table of elliptic curves

1975 = 5² · 79

Field	Data	Notes
Atkin-Lehner	5+ 79+	Signs for the Atkin-Lehner involutions
Class	1975b	Isogeny class
Conductor	1975	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	1234375 = 56 · 79	Discriminant
Eigenvalues	1  1 5+  1 -2 -3  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-51,123]	[a1,a2,a3,a4,a6]
Generators	[3:-1:1]	Generators of the group modulo torsion
j	912673/79	j-invariant
L	4.0847720113814	L(r)(E,1)/r!
Ω	2.6612788217922	Real period
R	1.5348906615619	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31600n1 126400e1 17775t1 79a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1975b1

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	1	+	1	-2	-3	6	4	-2	-6	-10	2	-10	-4	-7	-8	-3	-4	-8	15	-2	+	6	-7	19

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Quadratic twists for elliptic curve 1975b1

-4	8	-3	5	-7
31600n1	126400e1	17775t1	79a1	96775e1

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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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