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	12480bx	Isogeny class
Conductor	12480	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-3234816000000 = -1 · 216 · 35 · 56 · 13	Discriminant
Eigenvalues	2- 3+ 5+ -2  4 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2879,61921]	[a1,a2,a3,a4,a6]
Generators	[125:1536:1]	Generators of the group modulo torsion
j	40254822716/49359375	j-invariant
L	3.5736274897832	L(r)(E,1)/r!
Ω	0.53338336669359	Real period
R	3.3499615032391	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	12480bb1 3120i1 37440fv1 62400gj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480bx1

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
-	+	+	-2	4	-	0	2	2	-4	-4	2	-6	-4	-8	2	4	2	8	-8	-4	-8	12	6	4

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Quadratic twists for elliptic curve 12480bx1

-4	8	-3	5
12480bb1	3120i1	37440fv1	62400gj1

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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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