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	2470b	Isogeny class
Conductor	2470	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-126464000000000 = -1 · 218 · 59 · 13 · 19	Discriminant
Eigenvalues	2+  1 5+ -1  0 13-  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,11921,-203294]	[a1,a2,a3,a4,a6]
Generators	[525:4844:27]	Generators of the group modulo torsion
j	187376078091802391/126464000000000	j-invariant
L	2.5441821461174	L(r)(E,1)/r!
Ω	0.33303270435031	Real period
R	3.8197181731456	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	19760r3 79040s3 22230bt3 12350n3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2470b3

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	+	-1	0	-	0	-	6	-6	5	2	9	-10	-3	-6	-12	-1	-4	-9	2	-10	-15	-9	8

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Quadratic twists for elliptic curve 2470b3

-4	8	-3	5	-7	13	-19
19760r3	79040s3	22230bt3	12350n3	121030m3	32110z3	46930v3

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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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