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	48	Product of Tamagawa factors cp
Δ	968870113344 = 26 · 38 · 74 · 312	Discriminant
Eigenvalues	2- 3+ -2 7+  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-328104,-72474519]	[a1,a2,a3,a4,a6]
Generators	[2119:92495:1]	Generators of the group modulo torsion
j	3906235026100294102657/968870113344	j-invariant
L	3.0095643248171	L(r)(E,1)/r!
Ω	0.19947876601743	Real period
R	5.0290470925849	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	10416bl4 41664bt4 3906h4 32550bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302l3

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 1302l3

-4	8	-3	5	-7	-31
10416bl4	41664bt4	3906h4	32550bc4	9114y4	40362bd4

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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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