Cremona's table of elliptic curves

124950 = 2 · 3 · 5² · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	124950fy	Isogeny class
Conductor	124950	Conductor
∏ cp	672	Product of Tamagawa factors cp
deg	1032192	Modular degree for the optimal curve
Δ	-3882606336000000 = -1 · 214 · 32 · 56 · 73 · 173	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4488,2998281]	[a1,a2,a3,a4,a6]
Generators	[45:-1723:1] [-125:1337:1]	Generators of the group modulo torsion
j	-1865409391/724451328	j-invariant
L	14.869436477459	L(r)(E,1)/r!
Ω	0.35805681507946	Real period
R	0.24719135833894	Regulator
r	2	Rank of the group of rational points
S	0.99999999976337	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4998r1 124950hq1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 124950fy1

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
-	+	+	-	-4	-2	-	-4	-6	-10	-8	0	-6	8	4	-14	14	-14	-4	-10	14	4	-6	-2	2

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Quadratic twists for elliptic curve 124950fy1

5	-7
4998r1	124950hq1

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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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