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	1302b	Isogeny class
Conductor	1302	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	19545027428808 = 23 · 32 · 710 · 312	Discriminant
Eigenvalues	2+ 3+  4 7+ -2 -2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-11238,401580]	[a1,a2,a3,a4,a6]
j	156982476866335849/19545027428808	j-invariant
L	1.3228730117502	L(r)(E,1)/r!
Ω	0.66143650587509	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416bm2 41664bv2 3906r2 32550ck2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302b2

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

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Quadratic twists for elliptic curve 1302b2

-4	8	-3	5	-7	-31
10416bm2	41664bv2	3906r2	32550ck2	9114p2	40362o2

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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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