Cremona's table of elliptic curves

175 = 5² · 7

Field	Data	Notes
Atkin-Lehner	5- 7+	Signs for the Atkin-Lehner involutions
Class	175c	Isogeny class
Conductor	175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40	Modular degree for the optimal curve
Δ	-13671875 = -1 · 59 · 7	Discriminant
Eigenvalues	2  1 5- 7+ -3  1  7  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,42,-131]	[a1,a2,a3,a4,a6]
j	4096/7	j-invariant
L	2.3474425342029	L(r)(E,1)/r!
Ω	1.1737212671015	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	2800be1 11200bf1 1575i1 175a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 175c1

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 175c1

-4	8	-3	5	-7	-11	13	17	-19	-23
2800be1	11200bf1	1575i1	175a1	1225i1	21175bn1	29575w1	50575bh1	63175r1	92575bd1

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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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