Cremona's table of elliptic curves

5850 = 2 · 3² · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	5850q	Isogeny class
Conductor	5850	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	268800	Modular degree for the optimal curve
Δ	-4.1898334434762E+20	Discriminant
Eigenvalues	2+ 3- 5+  3  3 13- -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3197727,2412033741]	[a1,a2,a3,a4,a6]
Generators	[1950:58929:1]	Generators of the group modulo torsion
j	-198417696411528597145/22989483914821632	j-invariant
L	3.3651969669352	L(r)(E,1)/r!
Ω	0.16323199217897	Real period
R	1.0308019040917	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	46800eg1 1950y1 5850bw2 76050ev1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850q1

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	-	-3	0	-4	-5	-3	-12	-2	4	-3	-9	-15	-3	-7	8	-16	0	1	0	-2

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Quadratic twists for elliptic curve 5850q1

-4	-3	5	13
46800eg1	1950y1	5850bw2	76050ev1

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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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