Cremona's table of elliptic curves

2691 = 3² · 13 · 23

Field	Data	Notes
Atkin-Lehner	3- 13- 23+	Signs for the Atkin-Lehner involutions
Class	2691c	Isogeny class
Conductor	2691	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	586559961 = 38 · 132 · 232	Discriminant
Eigenvalues	1 3-  2  0  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-216,427]	[a1,a2,a3,a4,a6]
Generators	[66:487:1]	Generators of the group modulo torsion
j	1532808577/804609	j-invariant
L	4.2815017177137	L(r)(E,1)/r!
Ω	1.4338172122511	Real period
R	2.9860861490089	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	43056bv2 897c2 67275m2 34983c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2691c2

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	-	2	0	0	-	-6	-4	+	-6	0	2	6	-8	8	-2	-12	-10	-4	16	2	-4	0	6	-10

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Quadratic twists for elliptic curve 2691c2

-4	-3	5	13	-23
43056bv2	897c2	67275m2	34983c2	61893i2

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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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