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	12480cc	Isogeny class
Conductor	12480	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	215040	Modular degree for the optimal curve
Δ	192193560000 = 26 · 37 · 54 · 133	Discriminant
Eigenvalues	2- 3+ 5-  0 -4 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6406460,-6239168358]	[a1,a2,a3,a4,a6]
Generators	[-943478497527564778537884964652:-11733431483737563893768875:645778351520405058013325632]	Generators of the group modulo torsion
j	454357982636417669333824/3003024375	j-invariant
L	3.9054187627702	L(r)(E,1)/r!
Ω	0.094895369091489	Real period
R	41.154998396233	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	12480cu1 6240l2 37440dr1 62400ha1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480cc1

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	6	0	10	6	-4	0	-6	12	10	-12	12	-10	-8	16	14	-2

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Quadratic twists for elliptic curve 12480cc1

-4	8	-3	5
12480cu1	6240l2	37440dr1	62400ha1

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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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