Cremona's table of elliptic curves

575 = 5² · 23

Field	Data	Notes
Atkin-Lehner	5+ 23+	Signs for the Atkin-Lehner involutions
Class	575b	Isogeny class
Conductor	575	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-1123046875 = -1 · 511 · 23	Discriminant
Eigenvalues	-2  0 5+ -1  2  2 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,175,-1344]	[a1,a2,a3,a4,a6]
Generators	[45:312:1]	Generators of the group modulo torsion
j	37933056/71875	j-invariant
L	1.1252987905415	L(r)(E,1)/r!
Ω	0.80857956876877	Real period
R	0.34792456859099	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	9200z1 36800b1 5175n1 115a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 575b1

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	0	+	-1	2	2	-3	-2	+	7	-5	-11	1	0	0	-11	-13	-8	-5	5	-6	-12	-9	4	14

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Quadratic twists for elliptic curve 575b1

-4	8	-3	5	-7	-11	13	-23
9200z1	36800b1	5175n1	115a1	28175g1	69575h1	97175e1	13225f1

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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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