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	1302k	Isogeny class
Conductor	1302	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-36456 = -1 · 23 · 3 · 72 · 31	Discriminant
Eigenvalues	2- 3+  1 7+ -5 -5 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,0,9]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	-1/36456	j-invariant
L	3.2700144888835	L(r)(E,1)/r!
Ω	2.9081264774381	Real period
R	0.18740670979827	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10416bj1 41664bq1 3906f1 32550be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302k1

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
-	+	1	+	-5	-5	-3	-1	-6	10	-	-6	6	6	-9	2	-14	-5	3	13	-2	-5	-9	-6	-1

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Quadratic twists for elliptic curve 1302k1

-4	8	-3	5	-7	-31
10416bj1	41664bq1	3906f1	32550be1	9114x1	40362ba1

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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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