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	57800a	Isogeny class
Conductor	57800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-5.1292334125E+21	Discriminant
Eigenvalues	2+  0 5+  0  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,3735325,2037666750]	[a1,a2,a3,a4,a6]
Generators	[12073887777918477918570:-2234968186105236346859375:353516220116155368]	Generators of the group modulo torsion
j	7462174302/6640625	j-invariant
L	5.2829953474658	L(r)(E,1)/r!
Ω	0.088806733855117	Real period
R	29.744339860355	Regulator
r	1	Rank of the group of rational points
S	1.000000000022	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	115600a3 11560j4 3400a4	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 57800a3

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	+	0	0	2	+	-4	-8	-2	8	2	-2	4	0	-6	-4	6	-4	8	2	0	-4	-6	18

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Quadratic twists for elliptic curve 57800a3

-4	5	17
115600a3	11560j4	3400a4

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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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