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	1302l	Isogeny class
Conductor	1302	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-1015742988288 = -1 · 224 · 32 · 7 · 312	Discriminant
Eigenvalues	2- 3+ -2 7+  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-104,-48535]	[a1,a2,a3,a4,a6]
Generators	[39:73:1]	Generators of the group modulo torsion
j	-124475734657/1015742988288	j-invariant
L	3.0095643248171	L(r)(E,1)/r!
Ω	0.39895753203486	Real period
R	1.2572617731462	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10416bl1 41664bt1 3906h1 32550bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302l1

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	+	4	-2	-6	-4	0	-2	-	6	-6	-12	0	-10	4	-2	-12	-8	-14	-8	12	18	2

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Quadratic twists for elliptic curve 1302l1

-4	8	-3	5	-7	-31
10416bl1	41664bt1	3906h1	32550bc1	9114y1	40362bd1

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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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