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	12480o	Isogeny class
Conductor	12480	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	12480 = 26 · 3 · 5 · 13	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-260,-1530]	[a1,a2,a3,a4,a6]
Generators	[27:102:1]	Generators of the group modulo torsion
j	30488290624/195	j-invariant
L	4.2585990440444	L(r)(E,1)/r!
Ω	1.188549507864	Real period
R	3.5830220078065	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12480bh1 6240ba2 37440bk1 62400ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480o1

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

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Quadratic twists for elliptic curve 12480o1

-4	8	-3	5
12480bh1	6240ba2	37440bk1	62400ca1

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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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