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	2691h	Isogeny class
Conductor	2691	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	113637825724293 = 310 · 13 · 236	Discriminant
Eigenvalues	-1 3-  4  2  2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-48263,-4036566]	[a1,a2,a3,a4,a6]
j	17054173989052201/155881791117	j-invariant
L	1.9336928750203	L(r)(E,1)/r!
Ω	0.32228214583671	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	43056bs2 897a2 67275i2 34983k2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2691h2

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	-	-2	6	-	-2	4	4	6	0	0	-6	0	-2	-14	-12	14	8	-10	-16	4

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Quadratic twists for elliptic curve 2691h2

-4	-3	5	13	-23
43056bs2	897a2	67275i2	34983k2	61893m2

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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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