Cremona's table of elliptic curves

50864 = 2⁴ · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	50864k	Isogeny class
Conductor	50864	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-47660788736 = -1 · 210 · 115 · 172	Discriminant
Eigenvalues	2+  3 -3  0 11+ -4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1819,-31654]	[a1,a2,a3,a4,a6]
Generators	[1353:1486:27]	Generators of the group modulo torsion
j	-2249178948/161051	j-invariant
L	8.4778094094428	L(r)(E,1)/r!
Ω	0.36401960821283	Real period
R	5.8223576547689	Regulator
r	1	Rank of the group of rational points
S	0.99999999999846	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25432p1 50864z1	Quadratic twists by: -4 17

Hecke Eigenvalues for elliptic curve 50864k1

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
+	3	-3	0	+	-4	+	0	7	-2	0	3	-12	2	3	6	-9	10	8	8	4	10	0	-5	-18

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Quadratic twists for elliptic curve 50864k1

-4	17
25432p1	50864z1

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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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