Cremona's table of elliptic curves

1302 = 2 · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	1302g	Isogeny class
Conductor	1302	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-3499776 = -1 · 28 · 32 · 72 · 31	Discriminant
Eigenvalues	2+ 3- -2 7- -6  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-32,110]	[a1,a2,a3,a4,a6]
Generators	[0:10:1]	Generators of the group modulo torsion
j	-3463512697/3499776	j-invariant
L	2.1547060750481	L(r)(E,1)/r!
Ω	2.2773294980501	Real period
R	0.47307736471444	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	10416v1 41664t1 3906t1 32550bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302g1

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	-	-6	4	0	-4	6	-10	+	-2	-10	2	0	10	-12	-12	-8	12	-12	-14	0	0	14

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Quadratic twists for elliptic curve 1302g1

-4	8	-3	5	-7	-31
10416v1	41664t1	3906t1	32550bo1	9114h1	40362i1

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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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