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	12480i	Isogeny class
Conductor	12480	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-6469632000 = -1 · 214 · 35 · 53 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ -3  3 13- -1  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-421,5245]	[a1,a2,a3,a4,a6]
j	-504871936/394875	j-invariant
L	1.2271332499814	L(r)(E,1)/r!
Ω	1.2271332499814	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12480ct1 1560f1 37440cv1 62400cm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480i1

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
+	+	+	-3	3	-	-1	6	-5	6	2	-7	3	8	-2	1	0	15	-12	5	-6	-13	-12	1	17

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Quadratic twists for elliptic curve 12480i1

-4	8	-3	5
12480ct1	1560f1	37440cv1	62400cm1

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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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