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	12460c	Isogeny class
Conductor	12460	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	22680	Modular degree for the optimal curve
Δ	-1869778750000 = -1 · 24 · 57 · 75 · 89	Discriminant
Eigenvalues	2-  2 5+ 7-  5  4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-701,66410]	[a1,a2,a3,a4,a6]
j	-2384389341184/116861171875	j-invariant
L	3.4557184409307	L(r)(E,1)/r!
Ω	0.69114368818614	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	49840l1 112140p1 62300f1 87220p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12460c1

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	+	-	5	4	-3	-5	-3	-2	-8	7	3	9	9	-8	5	11	10	11	7	5	-6	-	-5

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Quadratic twists for elliptic curve 12460c1

-4	-3	5	-7
49840l1	112140p1	62300f1	87220p1

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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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