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	1302a	Isogeny class
Conductor	1302	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-1504839620100096 = -1 · 224 · 310 · 72 · 31	Discriminant
Eigenvalues	2+ 3+ -2 7+ -2  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,28579,171645]	[a1,a2,a3,a4,a6]
j	2581315285024874663/1504839620100096	j-invariant
L	0.57655240819323	L(r)(E,1)/r!
Ω	0.28827620409661	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416bk1 41664bs1 3906q1 32550cl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302a1

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	+	-2	4	0	-4	-6	-2	-	6	6	6	0	2	4	4	0	4	4	-2	0	0	14

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Quadratic twists for elliptic curve 1302a1

-4	8	-3	5	-7	-31
10416bk1	41664bs1	3906q1	32550cl1	9114l1	40362n1

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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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