Cremona's table of elliptic curves

575 = 5² · 23

Field	Data	Notes
Atkin-Lehner	5- 23+	Signs for the Atkin-Lehner involutions
Class	575c	Isogeny class
Conductor	575	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	280	Modular degree for the optimal curve
Δ	-44921875 = -1 · 59 · 23	Discriminant
Eigenvalues	2  2 5-  1  0  2 -5  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-458,3943]	[a1,a2,a3,a4,a6]
j	-5451776/23	j-invariant
L	4.0647452974081	L(r)(E,1)/r!
Ω	2.032372648704	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9200bj1 36800bk1 5175z1 575e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 575c1

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

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Quadratic twists for elliptic curve 575c1

-4	8	-3	5	-7	-11	13	-23
9200bj1	36800bk1	5175z1	575e1	28175z1	69575z1	97175q1	13225j1

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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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