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	192	Product of Tamagawa factors cp
Δ	15013703061504 = 212 · 34 · 72 · 314	Discriminant
Eigenvalues	2- 3+ -2 7+  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-20584,-1129879]	[a1,a2,a3,a4,a6]
Generators	[-77:115:1]	Generators of the group modulo torsion
j	964526913483831937/15013703061504	j-invariant
L	3.0095643248171	L(r)(E,1)/r!
Ω	0.39895753203486	Real period
R	2.5145235462925	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	10416bl2 41664bt2 3906h2 32550bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302l2

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 1302l2

-4	8	-3	5	-7	-31
10416bl2	41664bt2	3906h2	32550bc2	9114y2	40362bd2

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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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