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	3575a	Isogeny class
Conductor	3575	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	38008979658203125 = 510 · 116 · 133	Discriminant
Eigenvalues	0 -1 5+ -2 11+ 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-94583,6144693]	[a1,a2,a3,a4,a6]
Generators	[791:20630:1]	Generators of the group modulo torsion
j	9582250393600/3892119517	j-invariant
L	2.1102971082144	L(r)(E,1)/r!
Ω	0.33076863412299	Real period
R	3.1899897549381	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	57200bn2 32175n2 3575g2 39325h2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3575a2

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 3575a2

-4	-3	5	-11	13
57200bn2	32175n2	3575g2	39325h2	46475d2

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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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