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	12720bk	Isogeny class
Conductor	12720	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	640218562560 = 228 · 32 · 5 · 53	Discriminant
Eigenvalues	2- 3- 5- -4 -4  6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2160,-4140]	[a1,a2,a3,a4,a6]
Generators	[-21:180:1]	Generators of the group modulo torsion
j	272223782641/156303360	j-invariant
L	5.2428642370176	L(r)(E,1)/r!
Ω	0.76062112862944	Real period
R	3.4464361031258	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	1590p1 50880cf1 38160bk1 63600bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720bk1

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

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Quadratic twists for elliptic curve 12720bk1

-4	8	-3	5
1590p1	50880cf1	38160bk1	63600bo1

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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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