Cremona's table of elliptic curves

126075 = 3 · 5² · 41²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 41+	Signs for the Atkin-Lehner involutions
Class	126075j	Isogeny class
Conductor	126075	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1995840	Modular degree for the optimal curve
Δ	-95833709319993075 = -1 · 39 · 52 · 417	Discriminant
Eigenvalues	2 3+ 5+ -4  0  2 -5  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-316588,-70056687]	[a1,a2,a3,a4,a6]
Generators	[629207573993052:7514537491466009:874819998144]	Generators of the group modulo torsion
j	-29550530560/807003	j-invariant
L	8.2956831850881	L(r)(E,1)/r!
Ω	0.10047226854516	Real period
R	20.641723595001	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	126075bg1 3075j1	Quadratic twists by: 5 41

Hecke Eigenvalues for elliptic curve 126075j1

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	+	+	-4	0	2	-5	0	2	-5	0	3	+	7	-4	-1	-12	5	10	13	-9	2	12	-5	-8

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Quadratic twists for elliptic curve 126075j1

5	41
126075bg1	3075j1

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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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