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	12480cp	Isogeny class
Conductor	12480	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	14325948748800 = 210 · 316 · 52 · 13	Discriminant
Eigenvalues	2- 3- 5+ -4  0 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9181,282419]	[a1,a2,a3,a4,a6]
Generators	[-1:540:1]	Generators of the group modulo torsion
j	83587439220736/13990184325	j-invariant
L	4.5020637300804	L(r)(E,1)/r!
Ω	0.67161661802539	Real period
R	0.4189577440137	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	12480f1 3120f1 37440fi1 62400fd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480cp1

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

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Quadratic twists for elliptic curve 12480cp1

-4	8	-3	5
12480f1	3120f1	37440fi1	62400fd1

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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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