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	12720be	Isogeny class
Conductor	12720	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-18545760000000000 = -1 · 214 · 37 · 510 · 53	Discriminant
Eigenvalues	2- 3- 5+  4  6  6 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5304,6552180]	[a1,a2,a3,a4,a6]
j	4028027503031/4527773437500	j-invariant
L	4.238346382713	L(r)(E,1)/r!
Ω	0.30273902733664	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1590e1 50880cs1 38160bz1 63600bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720be1

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
-	-	+	4	6	6	-4	6	-4	-8	8	2	10	-12	2	-	6	8	4	8	-4	4	-12	6	2

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Quadratic twists for elliptic curve 12720be1

-4	8	-3	5
1590e1	50880cs1	38160bz1	63600bs1

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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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