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	1330f	Isogeny class
Conductor	1330	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-6650000 = -1 · 24 · 55 · 7 · 19	Discriminant
Eigenvalues	2+ -3 5- 7+  0 -4  1 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19,133]	[a1,a2,a3,a4,a6]
Generators	[2:9:1]	Generators of the group modulo torsion
j	-781229961/6650000	j-invariant
L	1.3036981774284	L(r)(E,1)/r!
Ω	2.0299033768556	Real period
R	0.064224642034334	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	10640ba1 42560d1 11970bt1 6650ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1330f1

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
+	-3	-	+	0	-4	1	-	-1	6	0	3	-7	-1	4	11	-6	8	-2	-15	3	-12	-12	-14	-10

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Quadratic twists for elliptic curve 1330f1

-4	8	-3	5	-7	-19
10640ba1	42560d1	11970bt1	6650ba1	9310b1	25270w1

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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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