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	5850ca	Isogeny class
Conductor	5850	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-64064520000 = -1 · 26 · 36 · 54 · 133	Discriminant
Eigenvalues	2- 3- 5- -1 -3 13- -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,895,-6703]	[a1,a2,a3,a4,a6]
Generators	[9:40:1]	Generators of the group modulo torsion
j	174196775/140608	j-invariant
L	5.5891219615153	L(r)(E,1)/r!
Ω	0.61253315005411	Real period
R	0.76038360277882	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	46800ff2 650g2 5850h2 76050cl2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850ca2

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
-	-	-	-1	-3	-	-3	-4	6	3	-1	2	0	-10	3	-3	15	-13	-13	0	-10	-4	-15	-6	-4

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Quadratic twists for elliptic curve 5850ca2

-4	-3	5	13
46800ff2	650g2	5850h2	76050cl2

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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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