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	5780b	Isogeny class
Conductor	5780	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	18360	Modular degree for the optimal curve
Δ	5580605952800000 = 28 · 55 · 178	Discriminant
Eigenvalues	2-  0 5+  2 -1  0 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-78608,-7683932]	[a1,a2,a3,a4,a6]
Generators	[-144:806:1]	Generators of the group modulo torsion
j	30081024/3125	j-invariant
L	3.7423166411562	L(r)(E,1)/r!
Ω	0.28703699851635	Real period
R	4.345916682634	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	23120v1 92480ch1 52020bk1 28900f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5780b1

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 5780b1

-4	8	-3	5	17
23120v1	92480ch1	52020bk1	28900f1	5780c1

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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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