Cremona's table of elliptic curves

1330 = 2 · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	1330g	Isogeny class
Conductor	1330	Conductor
∏ cp	35	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-543553252480 = -1 · 27 · 5 · 73 · 195	Discriminant
Eigenvalues	2-  0 5+ 7+ -1 -1 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3553,89777]	[a1,a2,a3,a4,a6]
Generators	[65:328:1]	Generators of the group modulo torsion
j	-4959007166945889/543553252480	j-invariant
L	3.4574724291103	L(r)(E,1)/r!
Ω	0.89940371846235	Real period
R	0.10983379823567	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	10640p1 42560x1 11970x1 6650g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1330g1

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
-	0	+	+	-1	-1	-3	-	-5	-9	-2	10	-3	-6	-12	8	-3	-9	3	9	2	7	-7	-10	-8

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Quadratic twists for elliptic curve 1330g1

-4	8	-3	5	-7	-19
10640p1	42560x1	11970x1	6650g1	9310r1	25270b1

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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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