Cremona's table of elliptic curves

175 = 5² · 7

Field	Data	Notes
Atkin-Lehner	5+ 7+	Signs for the Atkin-Lehner involutions
Class	175b	Isogeny class
Conductor	175	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-213623046875 = -1 · 515 · 7	Discriminant
Eigenvalues	0 -1 5+ 7+ -3 -5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3283,-74657]	[a1,a2,a3,a4,a6]
Generators	[397:7812:1]	Generators of the group modulo torsion
j	-250523582464/13671875	j-invariant
L	1.0476202635275	L(r)(E,1)/r!
Ω	0.31435146257085	Real period
R	0.83316000421928	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	2800s3 11200c3 1575e3 35a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 175b3

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	+	+	-3	-5	-3	2	6	3	-4	-2	-12	10	-9	-12	0	8	4	0	-2	-1	-12	-12	1

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Quadratic twists for elliptic curve 175b3

-4	8	-3	5	-7	-11	13	17	-19	-23
2800s3	11200c3	1575e3	35a2	1225a3	21175r3	29575h3	50575m3	63175d3	92575n3

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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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