Cremona's table of elliptic curves

72111 = 3 · 13 · 43²

Class	r	Atkin-Lehner	Eigenvalues
72111a (2 curves)	1	3+ 13+ 43+	1 3+  2  2  0 13+ -2 -2
Curve Equation t Generators 72111a1 [1,1,0,-747034,117942055] 2 [481820666271140427429468:3150438836069937378632401:603247454508276220096] 72111a2 [1,1,0,-5914989,-5458281390] 2 [43952418649389500283429431623414845125033870260:-8434521270156552324646189248960773939105641409525:1194426148533084395894250121535726779192384]
72111b (2 curves)	2	3+ 13+ 43-	1 3+ -2  0 -4 13+ -2  4
Curve Equation t Generators 72111b1 [1,1,0,-12981,3128400] 2 [2806:50369:8]&[1588:62374:1] 72111b2 [1,1,0,-410516,100683489] 2 [-176:13031:1]&[344:395:1]
72111c (2 curves)	2	3- 13+ 43+	-1 3- -2 -2  0 13+ -2  2
Curve Equation t Generators 72111c1 [1,0,0,-404,-1521] 2 [34:139:1]&[-9:42:1] 72111c2 [1,0,0,-3199,68354] 2 [-61:224:1]&[-55:308:1]
72111d (2 curves)	1	3- 13+ 43-	1 3- -2 -2 -2 13+ -6  2
Curve Equation t Generators 72111d1 [1,0,1,-12982,70235] 2 [14043:1657078:1] 72111d2 [1,0,1,-133167,-18630551] 2 [81908838:9662872015:5832]
72111e (4 curves)	0	3- 13- 43-	-1 3- -2  4  4 13-  2  0
Curve Equation t 72111e1 [1,0,0,886,21699] 2 72111e2 [1,0,0,-8359,252824] 4 72111e3 [1,0,0,-36094,-2393095] 2 72111e4 [1,0,0,-128544,17727723] 2

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

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