Cremona's table of elliptic curves

27744 = 2⁵ · 3 · 17²

Class	r	Atkin-Lehner	Eigenvalues
27744a (1 curve)	1	2+ 3+ 17+	2+ 3+  1  2  1 -1 17+  1
Curve Equation t Generators 27744a1 [0,-1,0,-40845,3207429] 1 [431:8092:1]
27744b (1 curve)	1	2+ 3+ 17+	2+ 3+  1 -2  5 -5 17+ -7
Curve Equation t Generators 27744b1 [0,-1,0,-63965,-17642187] 1 [1120171:19898228:2197]
27744c (1 curve)	1	2+ 3+ 17+	2+ 3+  1 -4  1  2 17+  4
Curve Equation t Generators 27744c1 [0,-1,0,40,-12] 1 [4:14:1]
27744d (2 curves)	1	2+ 3+ 17+	2+ 3+  2  2  0  2 17+ -4
Curve Equation t Generators 27744d1 [0,-1,0,-62,192] 2 [8:12:1] 27744d2 [0,-1,0,-232,-1100] 2 [25:90:1]
27744e (2 curves)	1	2+ 3+ 17+	2+ 3+ -2  2  0  2 17+  4
Curve Equation t Generators 27744e1 [0,-1,0,-18014,-835392] 2 [416:7968:1] 27744e2 [0,-1,0,-67144,5806984] 2 [1782544:31413591:4096]
27744f (4 curves)	1	2+ 3+ 17+	2+ 3+ -2  4 -4 -2 17+ -4
Curve Equation t Generators 27744f1 [0,-1,0,-674,3864] 4 [-26:56:1] 27744f2 [0,-1,0,2216,25828] 2 [57:578:1] 27744f3 [0,-1,0,-5009,-132255] 2 [53764:1551641:64] 27744f4 [0,-1,0,-9344,350664] 2 [841:24220:1]
27744g (1 curve)	0	2+ 3+ 17-	2+ 3+ -1 -4  1  2 17- -4
Curve Equation t 27744g1 [0,-1,0,11464,-10008] 1
27744h (2 curves)	0	2+ 3- 17+	2+ 3-  0 -2  0 -6 17+ -4
Curve Equation t 27744h1 [0,1,0,-132458,-18599280] 2 27744h2 [0,1,0,-129568,-19446628] 2
27744i (1 curve)	0	2+ 3- 17+	2+ 3-  1 -2 -1 -1 17+ -1
Curve Equation t 27744i1 [0,1,0,-40845,-3207429] 1
27744j (1 curve)	0	2+ 3- 17+	2+ 3-  1  4 -1  2 17+ -4
Curve Equation t 27744j1 [0,1,0,40,12] 1
27744k (2 curves)	0	2+ 3- 17+	2+ 3-  2 -2  0  2 17+  4
Curve Equation t 27744k1 [0,1,0,-62,-192] 2 27744k2 [0,1,0,-232,1100] 2
27744l (2 curves)	0	2+ 3- 17+	2+ 3- -2 -2  0  2 17+ -4
Curve Equation t 27744l1 [0,1,0,-18014,835392] 2 27744l2 [0,1,0,-67144,-5806984] 2
27744m (1 curve)	0	2+ 3- 17+	2+ 3-  3 -2  3  3 17+  5
Curve Equation t 27744m1 [0,1,0,771,107979] 1
27744n (1 curve)	1	2+ 3- 17-	2+ 3- -1  4 -1  2 17-  4
Curve Equation t Generators 27744n1 [0,1,0,11464,10008] 1 [46:798:1]
27744o (2 curves)	0	2- 3+ 17+	2- 3+  0  2  0 -6 17+  4
Curve Equation t 27744o1 [0,-1,0,-132458,18599280] 2 27744o2 [0,-1,0,-129568,19446628] 2
27744p (1 curve)	0	2- 3+ 17+	2- 3+ -1  2  5 -1 17+ -5
Curve Equation t 27744p1 [0,-1,0,79379,-1601531] 1
27744q (1 curve)	0	2- 3+ 17+	2- 3+  2  5  2 -1 17+  1
Curve Equation t 27744q1 [0,-1,0,-194882,33300132] 1
27744r (4 curves)	2	2- 3+ 17+	2- 3+ -2  0 -4 -2 17+  0
Curve Equation t Generators 27744r1 [0,-1,0,-29574,1945944] 4 [-181:1156:1]&[27:1080:1] 27744r2 [0,-1,0,-5009,5055873] 2 [-8855:-280908:125]&[-19:2268:1] 27744r3 [0,-1,0,-55584,-1965960] 2 [-199:1084:1]&[-147:1734:1] 27744r4 [0,-1,0,-471744,124869204] 4 [-228:14850:1]&[108:8670:1]
27744s (1 curve)	2	2- 3+ 17+	2- 3+ -2 -3  2 -5 17+ -3
Curve Equation t Generators 27744s1 [0,-1,0,6,-12] 1 [2:2:1]&[7:18:1]
27744t (1 curve)	0	2- 3+ 17+	2- 3+  3  2 -3  3 17+ -5
Curve Equation t 27744t1 [0,-1,0,771,-107979] 1
27744u (1 curve)	1	2- 3+ 17-	2- 3+  2 -3  2 -5 17-  3
Curve Equation t Generators 27744u1 [0,-1,0,1638,48948] 1 [8:250:1]
27744v (1 curve)	1	2- 3+ 17-	2- 3+ -2  5  2 -1 17- -1
Curve Equation t Generators 27744v1 [0,-1,0,-674,-6540] 1 [40:170:1]
27744w (1 curve)	1	2- 3- 17+	2- 3-  1  2 -5 -5 17+  7
Curve Equation t Generators 27744w1 [0,1,0,-63965,17642187] 1 [181:-3468:1]
27744x (1 curve)	1	2- 3- 17+	2- 3- -1 -2 -5 -1 17+  5
Curve Equation t Generators 27744x1 [0,1,0,79379,1601531] 1 [113:-3468:1]
27744y (1 curve)	1	2- 3- 17+	2- 3-  2 -5 -2 -1 17+ -1
Curve Equation t Generators 27744y1 [0,1,0,-194882,-33300132] 1 [63770:70158:125]
27744z (4 curves)	1	2- 3- 17+	2- 3- -2  0  4 -2 17+  0
Curve Equation t Generators 27744z1 [0,1,0,-29574,-1945944] 4 [100170:1302048:343] 27744z2 [0,1,0,-5009,-5055873] 4 [1063:34524:1] 27744z3 [0,1,0,-55584,1965960] 2 [-366:44506:27] 27744z4 [0,1,0,-471744,-124869204] 2 [1731460976:-47997038265:1404928]
27744ba (1 curve)	1	2- 3- 17+	2- 3- -2  3 -2 -5 17+  3
Curve Equation t Generators 27744ba1 [0,1,0,6,12] 1 [2:6:1]
27744bb (4 curves)	1	2- 3- 17+	2- 3- -2 -4  4 -2 17+  4
Curve Equation t Generators 27744bb1 [0,1,0,-674,-3864] 4 [-258:1144:27] 27744bb2 [0,1,0,2216,-25828] 2 [623:15606:1] 27744bb3 [0,1,0,-5009,132255] 2 [27:132:1] 27744bb4 [0,1,0,-9344,-350664] 2 [-3305679:576620:59319]
27744bc (1 curve)	0	2- 3- 17-	2- 3-  2  3 -2 -5 17- -3
Curve Equation t 27744bc1 [0,1,0,1638,-48948] 1
27744bd (1 curve)	2	2- 3- 17-	2- 3- -2 -5 -2 -1 17-  1
Curve Equation t Generators 27744bd1 [0,1,0,-674,6540] 1 [-23:102:1]&[-6:102:1]

Data from Elliptic Curve Data by J. E. Cremona.
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