Cremona's table of elliptic curves

50575 = 5² · 7 · 17²

Field	Data	Notes
Atkin-Lehner	5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	50575bf	Isogeny class
Conductor	50575	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	86736125 = 53 · 74 · 172	Discriminant
Eigenvalues	0 -2 5- 7- -1 -6 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-113,84]	[a1,a2,a3,a4,a6]
Generators	[-2:-18:1]	Generators of the group modulo torsion
j	4456448/2401	j-invariant
L	2.7979295629388	L(r)(E,1)/r!
Ω	1.6723581468933	Real period
R	0.20913055975325	Regulator
r	1	Rank of the group of rational points
S	0.99999999999898	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50575y1 50575bd1	Quadratic twists by: 5 17

Hecke Eigenvalues for elliptic curve 50575bf1

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
0	-2	-	-	-1	-6	+	5	6	3	0	-10	7	0	6	-6	15	-1	2	-9	-6	-11	-14	1	-8

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Quadratic twists for elliptic curve 50575bf1

5	17
50575y1	50575bd1

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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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