Cremona's table of elliptic curves

27200 = 2⁶ · 5² · 17

Class	r	Atkin-Lehner	Eigenvalues
27200a (4 curves)	1	2+ 5+ 17+	2+  0 5+  0  0 -2 17+  4
Curve Equation t Generators 27200a1 [0,0,0,-14300,658000] 2 [45:325:1] 27200a2 [0,0,0,-16300,462000] 4 [29:117:1] 27200a3 [0,0,0,51700,3318000] 2 [13629:1591317:1] 27200a4 [0,0,0,-116300,-14938000] 2 [-158859:174707:729]
27200b (2 curves)	1	2+ 5+ 17+	2+  0 5+  4 -2 -6 17+  0
Curve Equation t Generators 27200b1 [0,0,0,-2800,57000] 2 [-34:336:1] 27200b2 [0,0,0,-2300,78000] 2 [20:200:1]
27200c (4 curves)	1	2+ 5+ 17+	2+  0 5+ -4  0 -2 17+  4
Curve Equation t Generators 27200c1 [0,0,0,-1100,6000] 2 [-34:64:1] 27200c2 [0,0,0,-9100,-330000] 4 [-59:39:1] 27200c3 [0,0,0,-1100,-890000] 2 [190:2400:1] 27200c4 [0,0,0,-145100,-21274000] 2 [44760:1769300:27]
27200d (1 curve)	1	2+ 5+ 17+	2+  1 5+  2  0  5 17+  3
Curve Equation t Generators 27200d1 [0,1,0,6367,-155137] 1 [1011:10000:27]
27200e (1 curve)	1	2+ 5+ 17+	2+  1 5+  5 -4  3 17+  2
Curve Equation t Generators 27200e1 [0,1,0,86847,-1570657] 1 [565801:17025664:6859]
27200f (1 curve)	1	2+ 5+ 17+	2+ -1 5+ -1  4 -1 17+  6
Curve Equation t Generators 27200f1 [0,-1,0,-193,1217] 1 [1:32:1]
27200g (1 curve)	1	2+ 5+ 17+	2+ -1 5+ -2  0  5 17+ -3
Curve Equation t Generators 27200g1 [0,-1,0,6367,155137] 1 [32:625:1]
27200h (1 curve)	1	2+ 5+ 17+	2+ -1 5+ -2 -4 -1 17+  1
Curve Equation t Generators 27200h1 [0,-1,0,-33,-20063] 1 [57:-400:1]
27200i (2 curves)	1	2+ 5+ 17+	2+  2 5+  2 -2  2 17+  0
Curve Equation t Generators 27200i1 [0,-1,0,-13633,-604863] 2 [1256493:1451584:9261] 27200i2 [0,-1,0,-5633,-1316863] 2 [8427:140896:27]
27200j (2 curves)	1	2+ 5+ 17+	2+  2 5+ -2  0  2 17+  0
Curve Equation t Generators 27200j1 [0,-1,0,-12008,-507238] 2 [555895537986:87519153485125:22425768] 27200j2 [0,-1,0,-192633,-32477863] 2 [99152:31220925:1]
27200k (2 curves)	1	2+ 5+ 17+	2+  2 5+ -2  2  2 17+ -8
Curve Equation t Generators 27200k1 [0,-1,0,-354033,-80962063] 2 [368343747705:9319499513776:350402625] 27200k2 [0,-1,0,-352033,-81924063] 2 [401795151:24678750000:103823]
27200l (2 curves)	1	2+ 5+ 17+	2+ -2 5+  2  0  2 17+  0
Curve Equation t Generators 27200l1 [0,1,0,-12008,507238] 2 [53:150:1] 27200l2 [0,1,0,-192633,32477863] 2 [6771:1700:27]
27200m (2 curves)	1	2+ 5+ 17+	2+ -2 5+  2  2 -6 17+  8
Curve Equation t Generators 27200m1 [0,1,0,-12033,436063] 2 [18:475:1] 27200m2 [0,1,0,19967,2388063] 2 [-53:1088:1]
27200n (2 curves)	1	2+ 5+ 17+	2+ -2 5+  2  6  2 17+  0
Curve Equation t Generators 27200n1 [0,1,0,-433,1263] 2 [-22:25:1] 27200n2 [0,1,0,1567,11263] 2 [27:-272:1]
27200o (4 curves)	1	2+ 5+ 17+	2+ -2 5+ -2 -6  2 17+ -8
Curve Equation t Generators 27200o1 [0,1,0,-4085633,3177200863] 2 [1138:1675:1] 27200o2 [0,1,0,-3957633,3385712863] 2 [-1077:80000:1] 27200o3 [0,1,0,-6669633,-1306311137] 2 [5082596529:-54570254336:1860867] 27200o4 [0,1,0,26098367,-10317511137] 2 [315367203:31200000000:68921]
27200p (1 curve)	1	2+ 5+ 17+	2+  3 5+ -2  4 -3 17+ -3
Curve Equation t Generators 27200p1 [0,0,0,-16300,-802000] 1 [9480:163700:27]
27200q (1 curve)	1	2+ 5+ 17+	2+ -3 5+  1  4  3 17+ -6
Curve Equation t Generators 27200q1 [0,0,0,12500,1150000] 1 [54:1408:1]
27200r (2 curves)	0	2+ 5+ 17-	2+  0 5+  2  4  2 17-  4
Curve Equation t 27200r1 [0,0,0,-500,4000] 2 27200r2 [0,0,0,500,18000] 2
27200s (2 curves)	2	2+ 5+ 17-	2+  0 5+ -2 -4  2 17- -4
Curve Equation t Generators 27200s1 [0,0,0,-500,-4000] 2 [-14:16:1]&[-11:13:1] 27200s2 [0,0,0,500,-18000] 2 [36:216:1]&[54:408:1]
27200t (2 curves)	0	2+ 5+ 17-	2+  1 5+  1  0 -1 17-  4
Curve Equation t 27200t1 [0,1,0,47,-17] 1 27200t2 [0,1,0,-753,-8497] 1
27200u (2 curves)	0	2+ 5+ 17-	2+  1 5+ -2  0 -1 17-  1
Curve Equation t 27200u1 [0,1,0,638367,-60731137] 1 27200u2 [0,1,0,-10625633,-13764923137] 1
27200v (2 curves)	0	2+ 5+ 17-	2+  1 5+ -2  0  5 17-  1
Curve Equation t 27200v1 [0,1,0,-4033,412063] 1 27200v2 [0,1,0,35967,-10587937] 1
27200w (1 curve)	0	2+ 5+ 17-	2+  1 5+ -3  0 -5 17- -8
Curve Equation t 27200w1 [0,1,0,-208,-5162] 1
27200x (1 curve)	0	2+ 5+ 17-	2+ -1 5+  3  0 -5 17-  8
Curve Equation t 27200x1 [0,-1,0,-208,5162] 1
27200y (2 curves)	0	2+ 5+ 17-	2+  2 5+  0 -2 -6 17- -4
Curve Equation t 27200y1 [0,-1,0,-833,-6463] 2 27200y2 [0,-1,0,-4833,125537] 2
27200z (4 curves)	0	2+ 5+ 17-	2+ -2 5+  4 -6  2 17-  4
Curve Equation t 27200z1 [0,1,0,-4833,78463] 2 27200z2 [0,1,0,-68833,6926463] 2 27200z3 [0,1,0,-164833,-25809537] 2 27200z4 [0,1,0,-180833,-20513537] 2
27200ba (1 curve)	0	2+ 5+ 17-	2+  3 5+  2  4 -1 17-  7
Curve Equation t 27200ba1 [0,0,0,-544300,-155242000] 1
27200bb (1 curve)	2	2+ 5+ 17-	2+ -3 5+ -2 -4 -1 17- -7
Curve Equation t Generators 27200bb1 [0,0,0,-544300,155242000] 1 [-715:13375:1]&[4410:-289000:1]
27200bc (1 curve)	0	2+ 5- 17+	2+  1 5-  0  6  3 17+  7
Curve Equation t 27200bc1 [0,1,0,-1153,19423] 1
27200bd (1 curve)	0	2+ 5- 17+	2+  1 5- -3  0  5 17+  8
Curve Equation t 27200bd1 [0,1,0,-8,38] 1
27200be (1 curve)	0	2+ 5- 17+	2+  1 5- -4 -2  5 17+  7
Curve Equation t 27200be1 [0,1,0,-52833,-4993537] 1
27200bf (2 curves)	0	2+ 5- 17+	2+ -1 5- -1  0  1 17+  4
Curve Equation t 27200bf1 [0,-1,0,1167,-4463] 1 27200bf2 [0,-1,0,-18833,-1024463] 1
27200bg (1 curve)	0	2+ 5- 17+	2+ -1 5-  3  0  5 17+ -8
Curve Equation t 27200bg1 [0,-1,0,-8,-38] 1
27200bh (1 curve)	0	2+ 5- 17+	2+  3 5-  4  6  1 17+  1
Curve Equation t 27200bh1 [0,0,0,20,-400] 1
27200bi (1 curve)	2	2+ 5- 17+	2+ -3 5- -4 -6  1 17+ -1
Curve Equation t Generators 27200bi1 [0,0,0,20,400] 1 [-6:8:1]&[10:40:1]
27200bj (1 curve)	1	2+ 5- 17-	2+  1 5-  1  4  1 17-  6
Curve Equation t Generators 27200bj1 [0,1,0,-4833,142463] 1 [67:352:1]
27200bk (1 curve)	1	2+ 5- 17-	2+ -1 5-  0  6 -3 17-  7
Curve Equation t Generators 27200bk1 [0,-1,0,-28833,2485537] 1 [1017:32000:1]
27200bl (1 curve)	1	2+ 5- 17-	2+ -1 5-  4 -2 -5 17-  7
Curve Equation t Generators 27200bl1 [0,-1,0,-2113,-39103] 1 [67:340:1]
27200bm (1 curve)	1	2+ 5- 17-	2+ -1 5- -5 -4 -3 17-  2
Curve Equation t Generators 27200bm1 [0,-1,0,2171167,-200674463] 1 [9417:924800:1]
27200bn (1 curve)	1	2+ 5- 17-	2+  3 5- -1  4 -3 17- -6
Curve Equation t Generators 27200bn1 [0,0,0,500,9200] 1 [138:2944:27]
27200bo (1 curve)	1	2+ 5- 17-	2+  3 5-  4 -6 -1 17- -1
Curve Equation t Generators 27200bo1 [0,0,0,500,50000] 1 [-825:2125:27]
27200bp (1 curve)	1	2+ 5- 17-	2+ -3 5- -4  6 -1 17-  1
Curve Equation t Generators 27200bp1 [0,0,0,500,-50000] 1 [100:1000:1]
27200bq (4 curves)	0	2- 5+ 17+	2-  0 5+  0  0 -2 17+ -4
Curve Equation t 27200bq1 [0,0,0,-14300,-658000] 2 27200bq2 [0,0,0,-16300,-462000] 4 27200bq3 [0,0,0,51700,-3318000] 2 27200bq4 [0,0,0,-116300,14938000] 2
27200br (4 curves)	0	2- 5+ 17+	2-  0 5+  4  0 -2 17+ -4
Curve Equation t 27200br1 [0,0,0,-1100,-6000] 2 27200br2 [0,0,0,-9100,330000] 4 27200br3 [0,0,0,-1100,890000] 2 27200br4 [0,0,0,-145100,21274000] 2
27200bs (2 curves)	2	2- 5+ 17+	2-  0 5+ -4  2 -6 17+  0
Curve Equation t Generators 27200bs1 [0,0,0,-2800,-57000] 2 [-31:3:1]&[1010:10125:8] 27200bs2 [0,0,0,-2300,-78000] 2 [110:-1000:1]&[80:500:1]
27200bt (1 curve)	0	2- 5+ 17+	2-  1 5+  1  4  7 17+  6
Curve Equation t 27200bt1 [0,1,0,-108,398] 1
27200bu (1 curve)	0	2- 5+ 17+	2-  1 5+  1 -4 -1 17+ -6
Curve Equation t 27200bu1 [0,1,0,-193,-1217] 1
27200bv (1 curve)	0	2- 5+ 17+	2-  1 5+  2  4 -1 17+ -1
Curve Equation t 27200bv1 [0,1,0,-33,20063] 1
27200bw (1 curve)	0	2- 5+ 17+	2- -1 5+ -1 -4  7 17+ -6
Curve Equation t 27200bw1 [0,-1,0,-108,-398] 1
27200bx (1 curve)	0	2- 5+ 17+	2- -1 5+ -5  4  3 17+ -2
Curve Equation t 27200bx1 [0,-1,0,86847,1570657] 1
27200by (4 curves)	0	2- 5+ 17+	2-  2 5+  2  6  2 17+  8
Curve Equation t 27200by1 [0,-1,0,-4085633,-3177200863] 2 27200by2 [0,-1,0,-3957633,-3385712863] 2 27200by3 [0,-1,0,-6669633,1306311137] 2 27200by4 [0,-1,0,26098367,10317511137] 2
27200bz (2 curves)	0	2- 5+ 17+	2-  2 5+ -2  2  2 17+  4
Curve Equation t 27200bz1 [0,-1,0,-108,962] 2 27200bz2 [0,-1,0,-2233,41337] 2
27200ca (2 curves)	0	2- 5+ 17+	2-  2 5+ -2 -2 -6 17+ -8
Curve Equation t 27200ca1 [0,-1,0,-12033,-436063] 2 27200ca2 [0,-1,0,19967,-2388063] 2
27200cb (2 curves)	0	2- 5+ 17+	2-  2 5+ -2 -6  2 17+  0
Curve Equation t 27200cb1 [0,-1,0,-433,-1263] 2 27200cb2 [0,-1,0,1567,-11263] 2
27200cc (2 curves)	0	2- 5+ 17+	2- -2 5+  2 -2  2 17+ -4
Curve Equation t 27200cc1 [0,1,0,-108,-962] 2 27200cc2 [0,1,0,-2233,-41337] 2
27200cd (2 curves)	0	2- 5+ 17+	2- -2 5+  2 -2  2 17+  8
Curve Equation t 27200cd1 [0,1,0,-354033,80962063] 2 27200cd2 [0,1,0,-352033,81924063] 2
27200ce (2 curves)	0	2- 5+ 17+	2- -2 5+ -2  2  2 17+  0
Curve Equation t 27200ce1 [0,1,0,-13633,604863] 2 27200ce2 [0,1,0,-5633,1316863] 2
27200cf (1 curve)	0	2- 5+ 17+	2-  3 5+ -1 -4  3 17+  6
Curve Equation t 27200cf1 [0,0,0,12500,-1150000] 1
27200cg (1 curve)	2	2- 5+ 17+	2- -3 5+  2 -4 -3 17+  3
Curve Equation t Generators 27200cg1 [0,0,0,-16300,802000] 1 [10:800:1]&[-115:1075:1]
27200ch (2 curves)	1	2- 5+ 17-	2- -1 5+ -1  0 -1 17- -4
Curve Equation t Generators 27200ch1 [0,-1,0,47,17] 1 [1:8:1] 27200ch2 [0,-1,0,-753,8497] 1 [33:136:1]
27200ci (2 curves)	1	2- 5+ 17-	2- -1 5+  2  0 -1 17- -1
Curve Equation t Generators 27200ci1 [0,-1,0,638367,60731137] 1 [232:14875:1] 27200ci2 [0,-1,0,-10625633,13764923137] 1 [4752:265625:1]
27200cj (2 curves)	1	2- 5+ 17-	2- -1 5+  2  0  5 17- -1
Curve Equation t Generators 27200cj1 [0,-1,0,-4033,-412063] 1 [101:448:1] 27200cj2 [0,-1,0,35967,10587937] 1 [373:8704:1]
27200ck (2 curves)	1	2- 5+ 17-	2-  2 5+  4 -2  2 17- -8
Curve Equation t Generators 27200ck1 [0,-1,0,-633,6137] 2 [8:39:1] 27200ck2 [0,-1,0,-1633,-16863] 2 [-384:1547:27]
27200cl (4 curves)	1	2- 5+ 17-	2-  2 5+ -4  6  2 17- -4
Curve Equation t Generators 27200cl1 [0,-1,0,-4833,-78463] 2 [-19917:131300:729] 27200cl2 [0,-1,0,-68833,-6926463] 2 [-240272721:-50816332:1601613] 27200cl3 [0,-1,0,-164833,25809537] 2 [-339:6528:1] 27200cl4 [0,-1,0,-180833,20513537] 2 [3352:192525:1]
27200cm (2 curves)	1	2- 5+ 17-	2- -2 5+  0  2 -6 17-  4
Curve Equation t Generators 27200cm1 [0,1,0,-833,6463] 2 [-27:100:1] 27200cm2 [0,1,0,-4833,-125537] 2 [-43:68:1]
27200cn (2 curves)	1	2- 5+ 17-	2- -2 5+ -4  2  2 17-  8
Curve Equation t Generators 27200cn1 [0,1,0,-633,-6137] 2 [-13:8:1] 27200cn2 [0,1,0,-1633,16863] 2 [-17:200:1]
27200co (2 curves)	1	2- 5- 17+	2-  1 5-  1  0  1 17+ -4
Curve Equation t Generators 27200co1 [0,1,0,1167,4463] 1 [19:184:1] 27200co2 [0,1,0,-18833,1024463] 1 [83:200:1]
27200cp (1 curve)	1	2- 5- 17+	2- -1 5-  0 -6  3 17+ -7
Curve Equation t Generators 27200cp1 [0,-1,0,-1153,-19423] 1 [53:256:1]
27200cq (1 curve)	1	2- 5- 17+	2- -1 5-  4  2  5 17+ -7
Curve Equation t Generators 27200cq1 [0,-1,0,-52833,4993537] 1 [192:1375:1]
27200cr (1 curve)	0	2- 5- 17-	2-  1 5-  0 -6 -3 17- -7
Curve Equation t 27200cr1 [0,1,0,-28833,-2485537] 1
27200cs (1 curve)	0	2- 5- 17-	2-  1 5-  1 -4 -7 17- -6
Curve Equation t 27200cs1 [0,1,0,-2708,-55162] 1
27200ct (1 curve)	2	2- 5- 17-	2-  1 5- -4  2 -5 17- -7
Curve Equation t Generators 27200ct1 [0,1,0,-2113,39103] 1 [-33:272:1]&[18:85:1]
27200cu (1 curve)	0	2- 5- 17-	2-  1 5-  5  4 -3 17- -2
Curve Equation t 27200cu1 [0,1,0,2171167,200674463] 1
27200cv (1 curve)	0	2- 5- 17-	2- -1 5- -1  4 -7 17-  6
Curve Equation t 27200cv1 [0,-1,0,-2708,55162] 1
27200cw (1 curve)	0	2- 5- 17-	2- -1 5- -1 -4  1 17- -6
Curve Equation t 27200cw1 [0,-1,0,-4833,-142463] 1
27200cx (1 curve)	0	2- 5- 17-	2- -3 5-  1 -4 -3 17-  6
Curve Equation t 27200cx1 [0,0,0,500,-9200] 1

Data from Elliptic Curve Data by J. E. Cremona.
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Part of Computational Number Theory
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