Cremona's table of elliptic curves

57800 = 2³ · 5² · 17²

Field	Data	Notes
Atkin-Lehner	2- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	57800w	Isogeny class
Conductor	57800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	19652000000 = 28 · 56 · 173	Discriminant
Eigenvalues	2- -2 5+  2 -2  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-708,-2912]	[a1,a2,a3,a4,a6]
Generators	[-22:50:1] [-21:56:1]	Generators of the group modulo torsion
j	2000	j-invariant
L	7.7177193013729	L(r)(E,1)/r!
Ω	0.97478318088073	Real period
R	1.9793425483619	Regulator
r	2	Rank of the group of rational points
S	0.9999999999992	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	115600h1 2312a1 57800v1	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 57800w1

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

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Quadratic twists for elliptic curve 57800w1

-4	5	17
115600h1	2312a1	57800v1

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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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