Cremona's table of elliptic curves

2691 = 3² · 13 · 23

Field	Data	Notes
Atkin-Lehner	3+ 13- 23-	Signs for the Atkin-Lehner involutions
Conductor	2691	Conductor
Count	2	Number of curves in isogeny class
Curves	2691b1 2691b2	Curves in isogeny class
deg	192	Modular degree for the optimal curve
Eigenvalues	-1 3+  0  4  0 13- -6 -4	Hecke eigenvalues for primes less than 20
L	2.3521271564221	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	43056w 2691a 67275a 34983b	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for isogeny class 2691b

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

---

Quadratic twists for isogeny class 2691b

-4	-3	5	13	-23
43056w	2691a	67275a	34983b	61893b

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations