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	12480dh	Isogeny class
Conductor	12480	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2396160000 = 215 · 32 · 54 · 13	Discriminant
Eigenvalues	2- 3- 5- -4  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5025,135423]	[a1,a2,a3,a4,a6]
Generators	[42:15:1]	Generators of the group modulo torsion
j	428320044872/73125	j-invariant
L	5.600201625559	L(r)(E,1)/r!
Ω	1.4063270362078	Real period
R	1.991073726585	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	12480ci3 6240b3 37440es4 62400ek4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480dh4

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

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Quadratic twists for elliptic curve 12480dh4

-4	8	-3	5
12480ci3	6240b3	37440es4	62400ek4

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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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