Cremona's table of elliptic curves

2691 = 3² · 13 · 23

Class	r	Atkin-Lehner	Eigenvalues
2691a (2 curves)	0	3+ 13- 23+	1 3+  0  4  0 13-  6 -4
Curve Equation t 2691a1 [1,-1,0,-177,-856] 2 2691a2 [1,-1,0,-312,737] 2
2691b (2 curves)	1	3+ 13- 23-	-1 3+  0  4  0 13- -6 -4
Curve Equation t Generators 2691b1 [1,-1,1,-20,38] 2 [4:1:1] 2691b2 [1,-1,1,-35,-16] 2 [-2:7:1]
2691c (4 curves)	1	3- 13- 23+	1 3-  2  0  0 13- -6 -4
Curve Equation t Generators 2691c1 [1,-1,0,-171,904] 2 [20:62:1] 2691c2 [1,-1,0,-216,427] 4 [66:487:1] 2691c3 [1,-1,0,-1971,-32918] 2 [582:3329:8] 2691c4 [1,-1,0,819,2704] 2 [0:52:1]
2691d (4 curves)	0	3- 13- 23-	1 3- -2  4  0 13- -2  0
Curve Equation t 2691d1 [1,-1,0,-468,-4901] 2 2691d2 [1,-1,0,-8073,-277160] 4 2691d3 [1,-1,0,-129168,-17835935] 2 2691d4 [1,-1,0,-8658,-234221] 2
2691e (4 curves)	0	3- 13- 23-	1 3- -2 -4  4 13- -6 -8
Curve Equation t 2691e1 [1,-1,0,-176418,-28874961] 2 2691e2 [1,-1,0,-2833623,-1835242920] 4 2691e3 [1,-1,0,-45337968,-117489565665] 2 2691e4 [1,-1,0,-2844558,-1820356011] 4
2691f (2 curves)	0	3- 13- 23-	1 3-  4  2 -2 13-  6 -2
Curve Equation t 2691f1 [1,-1,0,0,243] 2 2691f2 [1,-1,0,-585,5508] 2
2691g (2 curves)	0	3- 13- 23-	-1 3-  0 -2  6 13-  6  2
Curve Equation t 2691g1 [1,-1,1,1177960,1612589114] 2 2691g2 [1,-1,1,-15530225,21481962716] 2
2691h (2 curves)	0	3- 13- 23-	-1 3-  4  2  2 13- -2  6
Curve Equation t 2691h1 [1,-1,1,-878,-150996] 2 2691h2 [1,-1,1,-48263,-4036566] 2

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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