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	975d	Isogeny class
Conductor	975	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-428466796875 = -1 · 33 · 513 · 13	Discriminant
Eigenvalues	-2 3+ 5+  1  5 13-  7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1658,-40282]	[a1,a2,a3,a4,a6]
j	-32278933504/27421875	j-invariant
L	0.72227521461287	L(r)(E,1)/r!
Ω	0.36113760730644	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15600cj1 62400cf1 2925l1 195c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975d1

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
-2	+	+	1	5	-	7	-6	-3	2	2	-7	9	8	-10	-5	0	5	4	9	6	-3	4	11	11

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Quadratic twists for elliptic curve 975d1

-4	8	-3	5	-7	-11	13
15600cj1	62400cf1	2925l1	195c1	47775cm1	117975j1	12675j1

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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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