Cremona's table of elliptic curves

3381 = 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	3- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	3381k	Isogeny class
Conductor	3381	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-210421001301 = -1 · 3 · 78 · 233	Discriminant
Eigenvalues	-1 3-  1 7+ -2  7 -3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1765,-36226]	[a1,a2,a3,a4,a6]
Generators	[85:613:1]	Generators of the group modulo torsion
j	-105484561/36501	j-invariant
L	2.8401806250436	L(r)(E,1)/r!
Ω	0.36196686102912	Real period
R	2.6155070448241	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	54096z1 10143h1 84525d1 3381f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3381k1

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	+	-2	7	-3	-8	-	-8	-6	6	-4	-4	-9	3	12	-2	1	9	3	-4	-18	10	0

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Quadratic twists for elliptic curve 3381k1

-4	-3	5	-7	-23
54096z1	10143h1	84525d1	3381f1	77763y1

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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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