Cremona's table of elliptic curves

7175 = 5² · 7 · 41

Field	Data	Notes
Atkin-Lehner	5+ 7+ 41+	Signs for the Atkin-Lehner involutions
Class	7175a	Isogeny class
Conductor	7175	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-351575 = -1 · 52 · 73 · 41	Discriminant
Eigenvalues	-1  1 5+ 7+  6  1  2 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,17,-8]	[a1,a2,a3,a4,a6]
Generators	[3:7:1]	Generators of the group modulo torsion
j	21653735/14063	j-invariant
L	3.1033207191196	L(r)(E,1)/r!
Ω	1.7313048726701	Real period
R	1.7924750100966	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	114800br1 64575r1 7175f1 50225k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7175a1

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
-1	1	+	+	6	1	2	-3	-1	-4	0	-3	+	-5	1	-2	-6	-4	8	2	-6	-2	0	-1	-1

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Quadratic twists for elliptic curve 7175a1

-4	-3	5	-7
114800br1	64575r1	7175f1	50225k1

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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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