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	5780d	Isogeny class
Conductor	5780	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-44644847622400 = -1 · 28 · 52 · 178	Discriminant
Eigenvalues	2-  0 5-  4 -2 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6647,383214]	[a1,a2,a3,a4,a6]
Generators	[-85:578:1]	Generators of the group modulo torsion
j	-5256144/7225	j-invariant
L	4.3193139538272	L(r)(E,1)/r!
Ω	0.57661868115526	Real period
R	1.248460520788	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	23120bc2 92480d2 52020w2 28900b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5780d2

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	-	4	-2	-6	+	0	0	6	-6	2	6	6	-10	-6	0	-10	-2	-6	-6	-6	6	-18	14

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Quadratic twists for elliptic curve 5780d2

-4	8	-3	5	17
23120bc2	92480d2	52020w2	28900b2	340a2

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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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