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	2691b	Isogeny class
Conductor	2691	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2413827 = 33 · 132 · 232	Discriminant
Eigenvalues	-1 3+  0  4  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-35,-16]	[a1,a2,a3,a4,a6]
Generators	[-2:7:1]	Generators of the group modulo torsion
j	170953875/89401	j-invariant
L	2.3521271564221	L(r)(E,1)/r!
Ω	2.0843905244878	Real period
R	0.56422420098078	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43056w2 2691a2 67275a2 34983b2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2691b2

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	+	0	4	0	-	-6	-4	-	-8	-2	10	-2	-6	0	-10	4	2	-4	0	6	-6	-12	8	18

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Quadratic twists for elliptic curve 2691b2

-4	-3	5	13	-23
43056w2	2691a2	67275a2	34983b2	61893b2

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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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