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	16	Product of Tamagawa factors cp
Δ	8718192 = 24 · 34 · 7 · 312	Discriminant
Eigenvalues	2+ 3- -2 7- -6  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-592,5486]	[a1,a2,a3,a4,a6]
Generators	[37:167:1]	Generators of the group modulo torsion
j	22889370414457/8718192	j-invariant
L	2.1547060750481	L(r)(E,1)/r!
Ω	2.2773294980501	Real period
R	0.23653868235722	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	10416v2 41664t2 3906t2 32550bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302g2

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 1302g2

-4	8	-3	5	-7	-31
10416v2	41664t2	3906t2	32550bo2	9114h2	40362i2

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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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