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	3344g	Isogeny class
Conductor	3344	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-18833408 = -1 · 213 · 112 · 19	Discriminant
Eigenvalues	2- -3 -2 -1 11+ -7 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-91,394]	[a1,a2,a3,a4,a6]
Generators	[-11:8:1] [-1:22:1]	Generators of the group modulo torsion
j	-20346417/4598	j-invariant
L	2.6070480043053	L(r)(E,1)/r!
Ω	2.0767599890218	Real period
R	0.15691798872324	Regulator
r	2	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	418c1 13376v1 30096be1 83600bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3344g1

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
-	-3	-2	-1	+	-7	-3	+	-3	1	-2	-6	-2	-4	0	3	-7	-12	-15	-6	-9	8	-16	-16	8

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Quadratic twists for elliptic curve 3344g1

-4	8	-3	5	-11	-19
418c1	13376v1	30096be1	83600bj1	36784bm1	63536ba1

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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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