Cremona's table of elliptic curves

75950 = 2 · 5² · 7² · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 31+	Signs for the Atkin-Lehner involutions
Class	75950de	Isogeny class
Conductor	75950	Conductor
∏ cp	104	Product of Tamagawa factors cp
deg	159744	Modular degree for the optimal curve
Δ	26142548992000 = 213 · 53 · 77 · 31	Discriminant
Eigenvalues	2- -1 5- 7- -3 -3 -2  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8233,145431]	[a1,a2,a3,a4,a6]
Generators	[-1:-392:1] [-85:532:1]	Generators of the group modulo torsion
j	4196653397/1777664	j-invariant
L	12.635560131988	L(r)(E,1)/r!
Ω	0.60441857870364	Real period
R	0.20101263392713	Regulator
r	2	Rank of the group of rational points
S	1.0000000000014	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75950bn1 10850bc1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 75950de1

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

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Quadratic twists for elliptic curve 75950de1

5	-7
75950bn1	10850bc1

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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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