Cremona's table of elliptic curves

575 = 5² · 23

Field	Data	Notes
Atkin-Lehner	5+ 23+	Signs for the Atkin-Lehner involutions
Class	575a	Isogeny class
Conductor	575	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	575 = 52 · 23	Discriminant
Eigenvalues	1  0 5+ -1 -1 -1  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	46305/23	j-invariant
L	2.3699937601478	L(r)(E,1)/r!
Ω	4.5838545933804	Real period
R	0.51703074603858	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	9200y1 36800a1 5175l1 575d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 575a1

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
1	0	+	-1	-1	-1	0	-5	+	-5	-2	4	-5	9	6	-2	8	-8	-8	-10	3	-3	-3	10	2

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Quadratic twists for elliptic curve 575a1

-4	8	-3	5	-7	-11	13	-23
9200y1	36800a1	5175l1	575d1	28175b1	69575f1	97175b1	13225c1

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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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