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	5850cc	Isogeny class
Conductor	5850	Conductor
∏ cp	324	Product of Tamagawa factors cp
Δ	-8648710200000000 = -1 · 29 · 39 · 58 · 133	Discriminant
Eigenvalues	2- 3- 5- -4  0 13-  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-756680,253575947]	[a1,a2,a3,a4,a6]
Generators	[-831:17965:1]	Generators of the group modulo torsion
j	-168256703745625/30371328	j-invariant
L	5.3424455628282	L(r)(E,1)/r!
Ω	0.4000297807117	Real period
R	0.37097554429596	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	46800fn2 1950m2 5850k2 76050ct2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5850cc2

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
-	-	-	-4	0	-	0	5	0	-3	-4	-7	-3	2	-9	-9	-6	8	5	3	-4	11	6	-6	8

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Quadratic twists for elliptic curve 5850cc2

-4	-3	5	13
46800fn2	1950m2	5850k2	76050ct2

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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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