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	1302j	Isogeny class
Conductor	1302	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	51726898829088 = 25 · 36 · 74 · 314	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-125397,-17140197]	[a1,a2,a3,a4,a6]
j	218064699967398378193/51726898829088	j-invariant
L	2.5370786581051	L(r)(E,1)/r!
Ω	0.25370786581051	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	10416bo3 41664bi4 3906b3 32550v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302j3

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

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Quadratic twists for elliptic curve 1302j3

-4	8	-3	5	-7	-31
10416bo3	41664bi4	3906b3	32550v4	9114ba3	40362bb4

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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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