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	16	Product of Tamagawa factors cp
Δ	2658140160000 = 223 · 3 · 54 · 132	Discriminant
Eigenvalues	2- 3- 5- -4  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5537825,-5017839777]	[a1,a2,a3,a4,a6]
Generators	[765824031:122255211000:29791]	Generators of the group modulo torsion
j	71647584155243142409/10140000	j-invariant
L	5.3100948547194	L(r)(E,1)/r!
Ω	0.098415780545295	Real period
R	13.488931412467	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	12480s4 3120o3 37440er4 62400ej4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480dg3

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 12480dg3

-4	8	-3	5
12480s4	3120o3	37440er4	62400ej4

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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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