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	12480co	Isogeny class
Conductor	12480	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	49152	Modular degree for the optimal curve
Δ	-213890625000000 = -1 · 26 · 34 · 512 · 132	Discriminant
Eigenvalues	2- 3- 5+  4  0 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,13044,-403506]	[a1,a2,a3,a4,a6]
Generators	[225:3738:1]	Generators of the group modulo torsion
j	3834800837445824/3342041015625	j-invariant
L	6.0038345841206	L(r)(E,1)/r!
Ω	0.30914968993433	Real period
R	4.8551193641792	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	12480bp1 6240z4 37440ff1 62400ff1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480co1

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

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Quadratic twists for elliptic curve 12480co1

-4	8	-3	5
12480bp1	6240z4	37440ff1	62400ff1

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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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