Cremona's table of elliptic curves

12480 = 2⁶ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	12480p	Isogeny class
Conductor	12480	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	-356441280 = -1 · 26 · 3 · 5 · 135	Discriminant
Eigenvalues	2+ 3+ 5- -1 -1 13- -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-135,1137]	[a1,a2,a3,a4,a6]
Generators	[32:169:1]	Generators of the group modulo torsion
j	-4283098624/5569395	j-invariant
L	3.9327275596291	L(r)(E,1)/r!
Ω	1.536348440761	Real period
R	0.51195776365433	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	12480bj1 6240j1 37440bo1 62400cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480p1

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	-	-3	-6	5	0	4	-5	7	6	-8	3	12	15	-8	-15	10	-1	-16	9	11

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Quadratic twists for elliptic curve 12480p1

-4	8	-3	5
12480bj1	6240j1	37440bo1	62400cd1

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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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