Cremona's table of elliptic curves

6975 = 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	3- 5+ 31+	Signs for the Atkin-Lehner involutions
Class	6975g	Isogeny class
Conductor	6975	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	5296640625 = 37 · 57 · 31	Discriminant
Eigenvalues	-1 3- 5+  4  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2255,41622]	[a1,a2,a3,a4,a6]
j	111284641/465	j-invariant
L	1.3657265629014	L(r)(E,1)/r!
Ω	1.3657265629014	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	111600fn1 2325b1 1395a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6975g1

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

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Quadratic twists for elliptic curve 6975g1

-4	-3	5
111600fn1	2325b1	1395a1

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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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