Cremona's table of elliptic curves

2470 = 2 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 13+ 19-	Signs for the Atkin-Lehner involutions
Class	2470c	Isogeny class
Conductor	2470	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-123500 = -1 · 22 · 53 · 13 · 19	Discriminant
Eigenvalues	2+ -1 5- -3  0 13+  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,16]	[a1,a2,a3,a4,a6]
Generators	[2:-6:1]	Generators of the group modulo torsion
j	-1771561/123500	j-invariant
L	1.913505249014	L(r)(E,1)/r!
Ω	2.7283451483434	Real period
R	0.11689046809051	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	19760u1 79040j1 22230bm1 12350t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2470c1

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	-	-3	0	+	4	-	2	6	9	-6	-7	-6	7	-10	-4	-5	-8	3	-10	14	-9	-1	-12

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Quadratic twists for elliptic curve 2470c1

-4	8	-3	5	-7	13	-19
19760u1	79040j1	22230bm1	12350t1	121030g1	32110v1	46930bm1

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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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