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	3344f	Isogeny class
Conductor	3344	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1016576 = 28 · 11 · 192	Discriminant
Eigenvalues	2- -2  2  0 11+  4 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-52,120]	[a1,a2,a3,a4,a6]
j	61918288/3971	j-invariant
L	1.3621506158243	L(r)(E,1)/r!
Ω	2.7243012316486	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	836b2 13376u2 30096bf2 83600bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3344f2

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	2	0	+	4	-2	+	4	8	-10	-6	12	4	12	-14	6	6	-6	-10	6	16	-4	2	14

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Quadratic twists for elliptic curve 3344f2

-4	8	-3	5	-11	-19
836b2	13376u2	30096bf2	83600bg2	36784bk2	63536w2

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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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