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	12720bd	Isogeny class
Conductor	12720	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	976896000 = 214 · 32 · 53 · 53	Discriminant
Eigenvalues	2- 3- 5+  4 -4  4 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2176,38324]	[a1,a2,a3,a4,a6]
j	278317173889/238500	j-invariant
L	3.1082376564825	L(r)(E,1)/r!
Ω	1.5541188282413	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	1590m1 50880cr1 38160by1 63600bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720bd1

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

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Quadratic twists for elliptic curve 12720bd1

-4	8	-3	5
1590m1	50880cr1	38160by1	63600bq1

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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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