Cremona's table of elliptic curves

12720 = 2⁴ · 3 · 5 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 53-	Signs for the Atkin-Lehner involutions
Class	12720bh	Isogeny class
Conductor	12720	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-6512640000 = -1 · 216 · 3 · 54 · 53	Discriminant
Eigenvalues	2- 3- 5-  0  0 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-480,-5772]	[a1,a2,a3,a4,a6]
Generators	[116:1230:1]	Generators of the group modulo torsion
j	-2992209121/1590000	j-invariant
L	5.9023861793016	L(r)(E,1)/r!
Ω	0.49750829351414	Real period
R	2.965973761769	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	1590o1 50880bx1 38160bf1 63600be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720bh1

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

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Quadratic twists for elliptic curve 12720bh1

-4	8	-3	5
1590o1	50880bx1	38160bf1	63600be1

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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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