Cremona's table of elliptic curves

3575 = 5² · 11 · 13

Field	Data	Notes
Atkin-Lehner	5- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	3575g	Isogeny class
Conductor	3575	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	2432574698125 = 54 · 116 · 133	Discriminant
Eigenvalues	0  1 5-  2 11+ 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3783,47644]	[a1,a2,a3,a4,a6]
Generators	[424:8651:1]	Generators of the group modulo torsion
j	9582250393600/3892119517	j-invariant
L	3.5087630253029	L(r)(E,1)/r!
Ω	0.73962115072376	Real period
R	0.79066673117478	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	57200cl2 32175y2 3575a2 39325s2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3575g2

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	1	-	2	+	-	-6	2	3	3	2	-4	0	-1	-6	3	-6	-7	-4	6	-4	-7	0	-12	8

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Quadratic twists for elliptic curve 3575g2

-4	-3	5	-11	13
57200cl2	32175y2	3575a2	39325s2	46475j2

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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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