Cremona's table of elliptic curves

12460 = 2² · 5 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 89-	Signs for the Atkin-Lehner involutions
Class	12460a	Isogeny class
Conductor	12460	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	15552	Modular degree for the optimal curve
Δ	1026134578000 = 24 · 53 · 78 · 89	Discriminant
Eigenvalues	2-  0 5+ 7+  0  6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2908,-35607]	[a1,a2,a3,a4,a6]
Generators	[-29:156:1]	Generators of the group modulo torsion
j	169975738220544/64133411125	j-invariant
L	4.0156328625516	L(r)(E,1)/r!
Ω	0.67101198019979	Real period
R	3.9896285819477	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	49840n1 112140l1 62300j1 87220m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12460a1

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

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Quadratic twists for elliptic curve 12460a1

-4	-3	5	-7
49840n1	112140l1	62300j1	87220m1

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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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