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	12480a	Isogeny class
Conductor	12480	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1560000000000000000 = -1 · 218 · 3 · 516 · 13	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-507521,-151415679]	[a1,a2,a3,a4,a6]
Generators	[56594497360:-878203917199:59776471]	Generators of the group modulo torsion
j	-55150149867714721/5950927734375	j-invariant
L	3.4058133531174	L(r)(E,1)/r!
Ω	0.088893233851016	Real period
R	19.156763712891	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	12480cj8 195a8 37440ca7 62400cs7	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480a8

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	-4	+	2	4	8	2	-8	-6	-6	4	-8	-6	12	2	4	0	-6	16	4	10	18

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Quadratic twists for elliptic curve 12480a8

-4	8	-3	5
12480cj8	195a8	37440ca7	62400cs7

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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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