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	12480bv	Isogeny class
Conductor	12480	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	63795363840 = 223 · 32 · 5 · 132	Discriminant
Eigenvalues	2- 3+ 5+  2  4 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-54561,4923585]	[a1,a2,a3,a4,a6]
Generators	[189:1152:1]	Generators of the group modulo torsion
j	68523370149961/243360	j-invariant
L	4.2872892296311	L(r)(E,1)/r!
Ω	0.96727458358874	Real period
R	1.1080848453922	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	12480bd2 3120x2 37440ft2 62400gn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480bv2

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

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Quadratic twists for elliptic curve 12480bv2

-4	8	-3	5
12480bd2	3120x2	37440ft2	62400gn2

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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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