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	5850bl	Isogeny class
Conductor	5850	Conductor
∏ cp	92	Product of Tamagawa factors cp
deg	30912	Modular degree for the optimal curve
Δ	-4346598968524800 = -1 · 223 · 313 · 52 · 13	Discriminant
Eigenvalues	2- 3- 5+  0 -4 13+  0  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-80915,9430067]	[a1,a2,a3,a4,a6]
Generators	[75:1906:1]	Generators of the group modulo torsion
j	-3214683778008145/238496514048	j-invariant
L	5.6791261916993	L(r)(E,1)/r!
Ω	0.42894057826511	Real period
R	0.1439118508399	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	46800cv1 1950f1 5850x1 76050bb1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850bl1

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	-4	+	0	1	-4	3	4	-5	-9	2	3	-1	-10	4	-9	-7	4	11	-6	-10	-12

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Quadratic twists for elliptic curve 5850bl1

-4	-3	5	13
46800cv1	1950f1	5850x1	76050bb1

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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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