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	975a	Isogeny class
Conductor	975	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22592197265625 = 34 · 510 · 134	Discriminant
Eigenvalues	1 3+ 5+  0  4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13000,-528125]	[a1,a2,a3,a4,a6]
Generators	[-642:959:8]	Generators of the group modulo torsion
j	15551989015681/1445900625	j-invariant
L	2.6002925141077	L(r)(E,1)/r!
Ω	0.44976814007551	Real period
R	5.7814066458133	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	15600bz3 62400cs4 2925g3 195a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975a3

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	+	-2	-4	-8	-2	-8	-6	-6	4	8	-6	-12	-2	4	0	6	16	4	10	-18

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Quadratic twists for elliptic curve 975a3

-4	8	-3	5	-7	-11	13
15600bz3	62400cs4	2925g3	195a3	47775cp4	117975p4	12675e3

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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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