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
deg	16	Modular degree for the optimal curve
Δ	-546875 = -1 · 57 · 7	Discriminant
Eigenvalues	0 -1 5+ 7+ -3 -5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-33,93]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	-262144/35	j-invariant
L	1.0476202635275	L(r)(E,1)/r!
Ω	2.8291631631377	Real period
R	0.092573333802142	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	2800s1 11200c1 1575e1 35a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 175b1

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 175b1

-4	8	-3	5	-7	-11	13	17	-19	-23
2800s1	11200c1	1575e1	35a3	1225a1	21175r1	29575h1	50575m1	63175d1	92575n1

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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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