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	2691f	Isogeny class
Conductor	2691	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-25502607 = -1 · 38 · 132 · 23	Discriminant
Eigenvalues	1 3-  4  2 -2 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,0,243]	[a1,a2,a3,a4,a6]
j	-1/34983	j-invariant
L	3.3695992132488	L(r)(E,1)/r!
Ω	1.6847996066244	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43056br1 897f1 67275j1 34983o1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2691f1

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	-	4	2	-2	-	6	-2	-	-2	0	-8	10	8	8	10	0	-10	-6	-4	-2	0	2	8	0

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Quadratic twists for elliptic curve 2691f1

-4	-3	5	13	-23
43056br1	897f1	67275j1	34983o1	61893j1

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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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