Cremona's table of elliptic curves

4199 = 13 · 17 · 19

Field	Data	Notes
Atkin-Lehner	13+ 17- 19+	Signs for the Atkin-Lehner involutions
Class	4199b	Isogeny class
Conductor	4199	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	36432	Modular degree for the optimal curve
Δ	-927081755719067 = -1 · 132 · 17 · 199	Discriminant
Eigenvalues	-2 -1  2 -4  0 13+ 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-116332,-15303422]	[a1,a2,a3,a4,a6]
j	-174110526670532497408/927081755719067	j-invariant
L	0.25842597390539	L(r)(E,1)/r!
Ω	0.1292129869527	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67184q1 37791d1 104975f1 54587c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4199b1

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
-2	-1	2	-4	0	+	-	+	-6	3	1	-10	-6	-9	11	2	-8	-4	-12	8	-2	8	-9	12	-1

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Quadratic twists for elliptic curve 4199b1

-4	-3	5	13	17	-19
67184q1	37791d1	104975f1	54587c1	71383b1	79781f1

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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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