Cremona's table of elliptic curves

3344 = 2⁴ · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 11- 19+	Signs for the Atkin-Lehner involutions
Class	3344h	Isogeny class
Conductor	3344	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-1016576 = -1 · 28 · 11 · 192	Discriminant
Eigenvalues	2-  1  1  0 11- -2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5,47]	[a1,a2,a3,a4,a6]
Generators	[11:38:1]	Generators of the group modulo torsion
j	-65536/3971	j-invariant
L	4.1207654152311	L(r)(E,1)/r!
Ω	2.2928970253935	Real period
R	0.44929682510753	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	836a1 13376o1 30096v1 83600bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3344h1

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	1	0	-	-2	-4	+	-1	-2	5	-3	0	-2	0	-10	3	-6	3	-5	0	4	4	1	-1

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Quadratic twists for elliptic curve 3344h1

-4	8	-3	5	-11	-19
836a1	13376o1	30096v1	83600bt1	36784bd1	63536bn1

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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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