Cremona's table of elliptic curves

3311 = 7 · 11 · 43

Field	Data	Notes
Atkin-Lehner	7+ 11+ 43+	Signs for the Atkin-Lehner involutions
Class	3311a	Isogeny class
Conductor	3311	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	832	Modular degree for the optimal curve
Δ	-48833939 = -1 · 74 · 11 · 432	Discriminant
Eigenvalues	2  1 -1 7+ 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,44,-303]	[a1,a2,a3,a4,a6]
Generators	[612:2075:64]	Generators of the group modulo torsion
j	9208180736/48833939	j-invariant
L	6.7042990142626	L(r)(E,1)/r!
Ω	1.0086249873312	Real period
R	1.6617422477313	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	52976bc1 29799f1 82775j1 23177a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3311a1

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	-1	+	+	2	-2	4	-9	6	-5	1	0	+	0	-6	-3	-8	-7	-1	-4	12	14	9	-7

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Quadratic twists for elliptic curve 3311a1

-4	-3	5	-7	-11
52976bc1	29799f1	82775j1	23177a1	36421g1

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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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