Cremona's table of elliptic curves

975 = 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	975g	Isogeny class
Conductor	975	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-609375 = -1 · 3 · 56 · 13	Discriminant
Eigenvalues	-1 3- 5+  4  4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,12,-33]	[a1,a2,a3,a4,a6]
j	12167/39	j-invariant
L	1.4788241842231	L(r)(E,1)/r!
Ω	1.4788241842231	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15600be1 62400bf1 2925f1 39a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975g1

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

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Quadratic twists for elliptic curve 975g1

-4	8	-3	5	-7	-11	13
15600be1	62400bf1	2925f1	39a4	47775u1	117975by1	12675w1

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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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