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	4	Product of Tamagawa factors cp
Δ	-43719326015625 = -1 · 316 · 57 · 13	Discriminant
Eigenvalues	1 3+ 5+  0  4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,5250,284625]	[a1,a2,a3,a4,a6]
Generators	[52158:4186083:8]	Generators of the group modulo torsion
j	1023887723039/2798036865	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	2	Number of elements in the torsion subgroup
Twists	15600bz4 62400cs3 2925g4 195a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975a4

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 975a4

-4	8	-3	5	-7	-11	13
15600bz4	62400cs3	2925g4	195a4	47775cp3	117975p3	12675e4

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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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