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	1302f	Isogeny class
Conductor	1302	Conductor
∏ cp	140	Product of Tamagawa factors cp
Δ	-1187360416300086 = -1 · 2 · 37 · 710 · 312	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,12473,-1567720]	[a1,a2,a3,a4,a6]
Generators	[94:614:1]	Generators of the group modulo torsion
j	214628074889266583/1187360416300086	j-invariant
L	2.1748197878149	L(r)(E,1)/r!
Ω	0.2441610108134	Real period
R	0.25449480249233	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416t2 41664q2 3906s2 32550bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302f2

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

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Quadratic twists for elliptic curve 1302f2

-4	8	-3	5	-7	-31
10416t2	41664q2	3906s2	32550bl2	9114f2	40362f2

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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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