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	1330d	Isogeny class
Conductor	1330	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-521360 = -1 · 24 · 5 · 73 · 19	Discriminant
Eigenvalues	2+  1 5+ 7-  0 -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-344,2422]	[a1,a2,a3,a4,a6]
Generators	[-11:75:1]	Generators of the group modulo torsion
j	-4483146738169/521360	j-invariant
L	2.2335447468672	L(r)(E,1)/r!
Ω	2.8181113641338	Real period
R	1.188851925066	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	10640j1 42560bl1 11970ch1 6650t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1330d1

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	3	-	-3	-6	-4	-1	-9	5	0	-9	6	-4	2	-9	-7	-4	0	6	2

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Quadratic twists for elliptic curve 1330d1

-4	8	-3	5	-7	-19
10640j1	42560bl1	11970ch1	6650t1	9310h1	25270t1

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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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