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	1330a	Isogeny class
Conductor	1330	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-5127312834560 = -1 · 216 · 5 · 77 · 19	Discriminant
Eigenvalues	2+ -1 5+ 7+  0  4  7 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,2517,98557]	[a1,a2,a3,a4,a6]
Generators	[-26:141:1]	Generators of the group modulo torsion
j	1762396940073671/5127312834560	j-invariant
L	1.6096608884959	L(r)(E,1)/r!
Ω	0.53925708693964	Real period
R	1.4924800503142	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	10640r1 42560bd1 11970bw1 6650x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1330a1

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	+	+	0	4	7	+	-5	2	-4	-5	-5	-1	0	-5	-14	-4	14	-7	5	4	-16	-10	10

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Quadratic twists for elliptic curve 1330a1

-4	8	-3	5	-7	-19
10640r1	42560bd1	11970bw1	6650x1	9310l1	25270n1

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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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