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	12480dg	Isogeny class
Conductor	12480	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	2771352327070679040 = 223 · 34 · 5 · 138	Discriminant
Eigenvalues	2- 3- 5- -4  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-397345,-53786785]	[a1,a2,a3,a4,a6]
Generators	[-286:6045:1]	Generators of the group modulo torsion
j	26465989780414729/10571870144160	j-invariant
L	5.3100948547194	L(r)(E,1)/r!
Ω	0.19683156109059	Real period
R	3.3722328531166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12480s3 3120o4 37440er3 62400ej3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480dg4

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	4	-8	-2	8	-2	-6	12	0	-10	0	10	-4	16	-6	8	-4	-14	-6

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Quadratic twists for elliptic curve 12480dg4

-4	8	-3	5
12480s3	3120o4	37440er3	62400ej3

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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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