Cremona's table of elliptic curves

54080 = 2⁶ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	54080cy	Isogeny class
Conductor	54080	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	718848	Modular degree for the optimal curve
Δ	2205735869584000000 = 210 · 56 · 1310	Discriminant
Eigenvalues	2-  1 5- -1 -3 13+ -3  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-723545,225614975]	[a1,a2,a3,a4,a6]
Generators	[-190:18875:1]	Generators of the group modulo torsion
j	296747776/15625	j-invariant
L	6.8590413498309	L(r)(E,1)/r!
Ω	0.25644599857725	Real period
R	4.45775549095	Regulator
r	1	Rank of the group of rational points
S	1.0000000000133	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54080bk1 13520r1 54080bz1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 54080cy1

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
-	1	-	-1	-3	+	-3	7	3	-3	-4	-7	9	11	0	6	3	-11	7	-3	-2	-8	12	-15	7

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Quadratic twists for elliptic curve 54080cy1

-4	8	13
54080bk1	13520r1	54080bz1

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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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