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	1330b	Isogeny class
Conductor	1330	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-85120 = -1 · 27 · 5 · 7 · 19	Discriminant
Eigenvalues	2+  2 5+ 7+ -3  1 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-408,3008]	[a1,a2,a3,a4,a6]
Generators	[11:-4:1]	Generators of the group modulo torsion
j	-7539913083529/85120	j-invariant
L	2.4864699210824	L(r)(E,1)/r!
Ω	3.0928099427024	Real period
R	0.8039517355243	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	10640s1 42560bg1 11970bz1 6650z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1330b1

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	+	+	-3	1	-5	+	1	-1	-4	4	-5	-4	-6	-8	1	-7	-7	-1	14	1	17	-10	10

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Quadratic twists for elliptic curve 1330b1

-4	8	-3	5	-7	-19
10640s1	42560bg1	11970bz1	6650z1	9310m1	25270o1

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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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