Cremona's table of elliptic curves

175 = 5² · 7

Field	Data	Notes
Atkin-Lehner	5- 7-	Signs for the Atkin-Lehner involutions
Class	175a	Isogeny class
Conductor	175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-875 = -1 · 53 · 7	Discriminant
Eigenvalues	-2 -1 5- 7- -3 -1 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,2,-2]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	4096/7	j-invariant
L	0.69773403150523	L(r)(E,1)/r!
Ω	2.6245205398761	Real period
R	0.13292599941667	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	2800y1 11200bo1 1575k1 175c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 175a1

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	-1	-	-	-3	-1	-7	0	-6	-5	2	-2	2	4	3	-6	10	-8	-2	-8	-6	-5	4	0	-7

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Quadratic twists for elliptic curve 175a1

-4	8	-3	5	-7	-11	13	17	-19	-23
2800y1	11200bo1	1575k1	175c1	1225j1	21175be1	29575r1	50575bc1	63175y1	92575ba1

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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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