Cremona's table of elliptic curves

10998 = 2 · 3² · 13 · 47

Class	r	Atkin-Lehner	Eigenvalues
10998a (2 curves)	2	2+ 3+ 13+ 47-	2+ 3+  0 -2 -4 13+ -8 -4
Curve Equation t Generators 10998a1 [1,-1,0,-42,-92] 2 [-3:2:1]&[12:26:1] 10998a2 [1,-1,0,-102,280] 2 [-10:20:1]&[-3:25:1]
10998b (4 curves)	1	2+ 3+ 13- 47-	2+ 3+  0  2  0 13-  0 -4
Curve Equation t Generators 10998b1 [1,-1,0,-84372,9454032] 6 [196780920:-151308452:1157625] 10998b2 [1,-1,0,-84612,9397728] 6 [18312:2468496:1] 10998b3 [1,-1,0,-94947,6942869] 2 [937:26734:1] 10998b4 [1,-1,0,-647907,-195551083] 2 [-442:2301:1]
10998c (1 curve)	1	2+ 3+ 13- 47-	2+ 3+  3 -3  4 13- -4  1
Curve Equation t Generators 10998c1 [1,-1,0,447,-67] 1 [1:19:1]
10998d (1 curve)	0	2+ 3- 13+ 47+	2+ 3- -2 -1  3 13+  6  6
Curve Equation t 10998d1 [1,-1,0,7407,-253391] 1
10998e (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  4  3  3 13+  0  2
Curve Equation t 10998e1 [1,-1,0,405,-1787] 1
10998f (1 curve)	1	2+ 3- 13+ 47-	2+ 3-  0 -3  1 13+  4 -2
Curve Equation t Generators 10998f1 [1,-1,0,-432,-3888] 1 [36:144:1]
10998g (1 curve)	1	2+ 3- 13+ 47-	2+ 3-  0  4 -4 13+  7  2
Curve Equation t Generators 10998g1 [1,-1,0,-2232,41152] 1 [29:-1:1]
10998h (1 curve)	1	2+ 3- 13+ 47-	2+ 3- -3 -5  2 13+ -2  5
Curve Equation t Generators 10998h1 [1,-1,0,54,-194] 1 [5:11:1]
10998i (2 curves)	0	2+ 3- 13- 47-	2+ 3-  0  2 -6 13- -3  2
Curve Equation t 10998i1 [1,-1,0,-522,-5076] 1 10998i2 [1,-1,0,3528,19710] 3
10998j (2 curves)	0	2- 3+ 13+ 47+	2- 3+  0 -2  4 13+  8 -4
Curve Equation t 10998j1 [1,-1,1,-380,2863] 2 10998j2 [1,-1,1,-920,-6641] 2
10998k (4 curves)	1	2- 3+ 13- 47+	2- 3+  0  2  0 13-  0 -4
Curve Equation t Generators 10998k1 [1,-1,1,-10550,-253627] 6 [213:2563:1] 10998k2 [1,-1,1,-71990,7266629] 6 [-303:1243:1] 10998k3 [1,-1,1,-759350,-254499515] 2 [-582234555:285899963:1157625] 10998k4 [1,-1,1,-761510,-252977147] 2 [-67645:114841:125]
10998l (1 curve)	1	2- 3+ 13- 47+	2- 3+ -3 -3 -4 13-  4  1
Curve Equation t Generators 10998l1 [1,-1,1,4021,-2213] 1 [115:-1462:1]
10998m (4 curves)	1	2- 3- 13+ 47+	2- 3- -2  0  0 13+  6 -4
Curve Equation t Generators 10998m1 [1,-1,1,-536,-3045] 2 [-7:21:1] 10998m2 [1,-1,1,-3416,75291] 4 [-49:375:1] 10998m3 [1,-1,1,-54176,4867035] 2 [135:-61:1] 10998m4 [1,-1,1,1264,262491] 2 [-37:423:1]
10998n (2 curves)	0	2- 3- 13+ 47-	2- 3- -2  2  0 13+ -6 -2
Curve Equation t 10998n1 [1,-1,1,-1121,-14479] 2 10998n2 [1,-1,1,-18041,-928159] 2
10998o (1 curve)	0	2- 3- 13+ 47-	2- 3-  4  2  6 13+ -3 -2
Curve Equation t 10998o1 [1,-1,1,44572,-23307001] 1
10998p (2 curves)	1	2- 3- 13- 47-	2- 3-  0  0  0 13-  6 -2
Curve Equation t Generators 10998p1 [1,-1,1,-815,-89161] 2 [87:658:1] 10998p2 [1,-1,1,-35375,-2536009] 2 [-111:172:1]
10998q (1 curve)	1	2- 3- 13- 47-	2- 3-  1  1  2 13- -6 -3
Curve Equation t Generators 10998q1 [1,-1,1,-392,3147] 1 [5:33:1]
10998r (1 curve)	1	2- 3- 13- 47-	2- 3-  1  3 -6 13- -2  3
Curve Equation t Generators 10998r1 [1,-1,1,-4037,114117] 1 [221:3048:1]
10998s (1 curve)	1	2- 3- 13- 47-	2- 3-  2 -3 -3 13-  2 -2
Curve Equation t Generators 10998s1 [1,-1,1,-121559,16343151] 1 [203:-138:1]
10998t (1 curve)	1	2- 3- 13- 47-	2- 3- -2 -3 -3 13- -2  6
Curve Equation t Generators 10998t1 [1,-1,1,1089814,-411210903] 1 [8399:771159:1]
10998u (1 curve)	1	2- 3- 13- 47-	2- 3- -4  0  0 13- -1 -2
Curve Equation t Generators 10998u1 [1,-1,1,58,-75] 1 [5:15:1]
10998v (1 curve)	1	2- 3- 13- 47-	2- 3- -4  1 -3 13-  4  2
Curve Equation t Generators 10998v1 [1,-1,1,9796018,24017532765] 1 [2567:255765:1]

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