Cremona's table of elliptic curves

12810 = 2 · 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	12810o	Isogeny class
Conductor	12810	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	102480 = 24 · 3 · 5 · 7 · 61	Discriminant
Eigenvalues	2- 3+ 5- 7+  4 -6  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-546560,-155754415]	[a1,a2,a3,a4,a6]
j	18056654814734214819841/102480	j-invariant
L	2.8093773198125	L(r)(E,1)/r!
Ω	0.17558608248828	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	102480co4 38430j4 64050be4 89670ca4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12810o3

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
-	+	-	+	4	-6	6	-8	0	-2	8	-6	-6	12	0	-2	0	-	4	16	-10	12	-4	2	14

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Quadratic twists for elliptic curve 12810o3

-4	-3	5	-7
102480co4	38430j4	64050be4	89670ca4

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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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