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	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	8073 = 33 · 13 · 23	Discriminant
Eigenvalues	-1 3+  0  4  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-20,38]	[a1,a2,a3,a4,a6]
Generators	[4:1:1]	Generators of the group modulo torsion
j	31255875/299	j-invariant
L	2.3521271564221	L(r)(E,1)/r!
Ω	4.1687810489757	Real period
R	1.1284484019616	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	43056w1 2691a1 67275a1 34983b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 2691b1

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 2691b1

-4	-3	5	13	-23
43056w1	2691a1	67275a1	34983b1	61893b1

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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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