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	3381a	Isogeny class
Conductor	3381	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-699867 = -1 · 33 · 72 · 232	Discriminant
Eigenvalues	0 3+  0 7-  6 -5  6  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-303,-1933]	[a1,a2,a3,a4,a6]
j	-62992384000/14283	j-invariant
L	1.1439673061191	L(r)(E,1)/r!
Ω	0.57198365305957	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	54096dg1 10143q1 84525cg1 3381i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3381a1

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
0	+	0	-	6	-5	6	1	+	6	-5	-7	0	-1	-6	12	6	-14	5	-6	7	5	12	6	10

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Quadratic twists for elliptic curve 3381a1

-4	-3	5	-7	-23
54096dg1	10143q1	84525cg1	3381i1	77763c1

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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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