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	12480db	Isogeny class
Conductor	12480	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-3744000000000000 = -1 · 217 · 32 · 512 · 13	Discriminant
Eigenvalues	2- 3- 5-  0  0 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-865,-2944225]	[a1,a2,a3,a4,a6]
Generators	[545:12600:1]	Generators of the group modulo torsion
j	-546718898/28564453125	j-invariant
L	6.1481644701395	L(r)(E,1)/r!
Ω	0.20199062942196	Real period
R	2.5364891462762	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	12480n4 3120a4 37440ec3 62400dx3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480db4

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

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Quadratic twists for elliptic curve 12480db4

-4	8	-3	5
12480n4	3120a4	37440ec3	62400dx3

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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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