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	3388d	Isogeny class
Conductor	3388	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	38016	Modular degree for the optimal curve
Δ	-3479833396998269696 = -1 · 28 · 78 · 119	Discriminant
Eigenvalues	2-  1  1 7- 11+  0  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,241355,-77200169]	[a1,a2,a3,a4,a6]
Generators	[645:18634:1]	Generators of the group modulo torsion
j	2575826944/5764801	j-invariant
L	4.2258802916729	L(r)(E,1)/r!
Ω	0.12982516581229	Real period
R	0.67813641671351	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	13552j1 54208w1 30492x1 84700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3388d1

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	0	-8	-3	-8	1	3	-8	-8	4	6	-9	8	3	7	-8	0	8	7	-7

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Quadratic twists for elliptic curve 3388d1

-4	8	-3	5	-7	-11
13552j1	54208w1	30492x1	84700c1	23716b1	3388a1

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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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