Cremona's table of elliptic curves

3388 = 2² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 7- 11-	Signs for the Atkin-Lehner involutions
Class	3388f	Isogeny class
Conductor	3388	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-244447073024 = -1 · 28 · 72 · 117	Discriminant
Eigenvalues	2- -1 -1 7- 11-  4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2581,-54943]	[a1,a2,a3,a4,a6]
j	-4194304/539	j-invariant
L	1.330035328252	L(r)(E,1)/r!
Ω	0.33250883206301	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	13552o1 54208bg1 30492bf1 84700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3388f1

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	-	-	4	6	2	1	-2	-1	-9	-6	-8	-8	10	1	2	11	11	14	14	-4	13	-9

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Quadratic twists for elliptic curve 3388f1

-4	8	-3	5	-7	-11
13552o1	54208bg1	30492bf1	84700h1	23716f1	308a1

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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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