Cremona's table of elliptic curves

5780 = 2² · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 5- 17+	Signs for the Atkin-Lehner involutions
Class	5780c	Isogeny class
Conductor	5780	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	231200000 = 28 · 55 · 172	Discriminant
Eigenvalues	2-  0 5- -2  1  0 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-272,-1564]	[a1,a2,a3,a4,a6]
Generators	[-8:10:1]	Generators of the group modulo torsion
j	30081024/3125	j-invariant
L	3.844220796483	L(r)(E,1)/r!
Ω	1.1834838633432	Real period
R	0.21654827274809	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	23120ba1 92480b1 52020u1 28900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5780c1

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	-	-2	1	0	+	3	0	3	0	2	-9	-6	2	6	-3	-1	-2	9	6	3	-6	-3	2

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Quadratic twists for elliptic curve 5780c1

-4	8	-3	5	17
23120ba1	92480b1	52020u1	28900a1	5780b1

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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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