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	12460b	Isogeny class
Conductor	12460	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-9869566000 = -1 · 24 · 53 · 7 · 893	Discriminant
Eigenvalues	2- -2 5+ 7-  3 -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,419,3600]	[a1,a2,a3,a4,a6]
Generators	[0:60:1]	Generators of the group modulo torsion
j	507234615296/616847875	j-invariant
L	2.8109645611425	L(r)(E,1)/r!
Ω	0.86377953222229	Real period
R	3.2542615983394	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	49840k2 112140r2 62300c2 87220r2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12460b2

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
-	-2	+	-	3	-4	-3	-1	-3	-6	8	-7	9	5	3	0	9	5	14	-15	-1	-1	-6	+	-13

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Quadratic twists for elliptic curve 12460b2

-4	-3	5	-7
49840k2	112140r2	62300c2	87220r2

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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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