Cremona's table of elliptic curves

34200 = 2³ · 3² · 5² · 19

Class	r	Atkin-Lehner	Eigenvalues
34200a (2 curves)	1	2+ 3+ 5+ 19+	2+ 3+ 5+  0  2  0  0 19+
Curve Equation t Generators 34200a1 [0,0,0,-2673675,-1682714250] 2 [432580700257569:-1005506271876214368:80062991] 34200a2 [0,0,0,-2700675,-1646993250] 2 [-518177010:89464825:474552]
34200b (2 curves)	1	2+ 3+ 5+ 19+	2+ 3+ 5+  0 -6 -2 -4 19+
Curve Equation t Generators 34200b1 [0,0,0,-450,-4375] 2 [44:247:1] 34200b2 [0,0,0,-7575,-253750] 2 [119:728:1]
34200c (1 curve)	1	2+ 3+ 5+ 19+	2+ 3+ 5+ -1  2  4 -2 19+
Curve Equation t Generators 34200c1 [0,0,0,-375,2795] 1 [11:1:1]
34200d (1 curve)	1	2+ 3+ 5+ 19+	2+ 3+ 5+ -1  4 -6  0 19+
Curve Equation t Generators 34200d1 [0,0,0,-15,-5] 1 [-1:3:1]
34200e (2 curves)	1	2+ 3+ 5+ 19+	2+ 3+ 5+  2 -2  0 -6 19+
Curve Equation t Generators 34200e1 [0,0,0,5925,20179750] 2 [1695:70000:1] 34200e2 [0,0,0,-1077075,421972750] 2 [2770:76125:8]
34200f (1 curve)	1	2+ 3+ 5+ 19+	2+ 3+ 5+  3  2  0 -6 19+
Curve Equation t Generators 34200f1 [0,0,0,-16875,759375] 1 [99:243:1]
34200g (2 curves)	1	2+ 3+ 5+ 19+	2+ 3+ 5+ -4  2  4  4 19+
Curve Equation t Generators 34200g1 [0,0,0,-12075,-510250] 2 [1471:56256:1] 34200g2 [0,0,0,-15075,-237250] 2 [-110:300:1]
34200h (1 curve)	1	2+ 3+ 5+ 19+	2+ 3+ 5+ -5 -4  2 -4 19+
Curve Equation t Generators 34200h1 [0,0,0,-91875,-10715625] 1 [-174:51:1]
34200i (2 curves)	0	2+ 3+ 5+ 19-	2+ 3+ 5+  0 -2  2  4 19-
Curve Equation t 34200i1 [0,0,0,-375,-1750] 2 34200i2 [0,0,0,1125,-12250] 2
34200j (1 curve)	0	2+ 3+ 5- 19+	2+ 3+ 5-  1 -2 -4 -2 19+
Curve Equation t 34200j1 [0,0,0,-84375,-9433125] 1
34200k (1 curve)	0	2+ 3+ 5- 19+	2+ 3+ 5-  1 -4  6  0 19+
Curve Equation t 34200k1 [0,0,0,-3375,16875] 1
34200l (2 curves)	0	2+ 3+ 5- 19+	2+ 3+ 5-  2 -2 -6  2 19+
Curve Equation t 34200l1 [0,0,0,-810,-8775] 2 34200l2 [0,0,0,-135,-22950] 2
34200m (2 curves)	0	2+ 3+ 5- 19+	2+ 3+ 5- -2  2  6  2 19+
Curve Equation t 34200m1 [0,0,0,-2250,40625] 2 34200m2 [0,0,0,-375,106250] 2
34200n (1 curve)	2	2+ 3+ 5- 19+	2+ 3+ 5- -3 -2  0 -6 19+
Curve Equation t Generators 34200n1 [0,0,0,-75,-225] 1 [-6:3:1]&[-5:5:1]
34200o (1 curve)	0	2+ 3+ 5- 19+	2+ 3+ 5-  5  4 -2 -4 19+
Curve Equation t 34200o1 [0,0,0,-33075,2314575] 1
34200p (4 curves)	0	2+ 3- 5+ 19+	2+ 3- 5+  0  0 -2  2 19+
Curve Equation t 34200p1 [0,0,0,-38775,2938250] 2 34200p2 [0,0,0,-43275,2213750] 4 34200p3 [0,0,0,127725,15380750] 2 34200p4 [0,0,0,-286275,-57321250] 2
34200q (4 curves)	0	2+ 3- 5+ 19+	2+ 3- 5+  0 -4 -2  6 19+
Curve Equation t 34200q1 [0,0,0,4425,-197750] 2 34200q2 [0,0,0,-36075,-2182250] 4 34200q3 [0,0,0,-171075,25222750] 2 34200q4 [0,0,0,-549075,-156595250] 2
34200r (1 curve)	0	2+ 3- 5+ 19+	2+ 3- 5+  1 -4 -1 -7 19+
Curve Equation t 34200r1 [0,0,0,-15075,-3125250] 1
34200s (1 curve)	0	2+ 3- 5+ 19+	2+ 3- 5+ -1  0  0  4 19+
Curve Equation t 34200s1 [0,0,0,-44535,3502235] 1
34200t (1 curve)	0	2+ 3- 5+ 19+	2+ 3- 5+ -1 -4  4 -8 19+
Curve Equation t 34200t1 [0,0,0,-538455,-152080045] 1
34200u (1 curve)	0	2+ 3- 5+ 19+	2+ 3- 5+  2  1 -6 -6 19+
Curve Equation t 34200u1 [0,0,0,-5475,-201170] 1
34200v (2 curves)	0	2+ 3- 5+ 19+	2+ 3- 5+  2  2  4 -2 19+
Curve Equation t 34200v1 [0,0,0,4425,562250] 2 34200v2 [0,0,0,-81075,8342750] 2
34200w (1 curve)	0	2+ 3- 5+ 19+	2+ 3- 5+  3  3  4  5 19+
Curve Equation t 34200w1 [0,0,0,-300,-11500] 1
34200x (2 curves)	0	2+ 3- 5+ 19+	2+ 3- 5+ -4  4  0  6 19+
Curve Equation t 34200x1 [0,0,0,1050,-5375] 2 34200x2 [0,0,0,-4575,-44750] 2
34200y (2 curves)	0	2+ 3- 5+ 19+	2+ 3- 5+ -4 -4  4 -2 19+
Curve Equation t 34200y1 [0,0,0,-5857950,5461639625] 2 34200y2 [0,0,0,-93748575,349377655250] 2
34200z (4 curves)	1	2+ 3- 5+ 19-	2+ 3- 5+  0  0  2 -6 19-
Curve Equation t Generators 34200z1 [0,0,0,-21450,-2363375] 2 [1724:71307:1] 34200z2 [0,0,0,-427575,-107549750] 4 [47973:1859264:27] 34200z3 [0,0,0,-513075,-61465250] 2 [-190:5400:1] 34200z4 [0,0,0,-6840075,-6885562250] 2 [108958938:565249616:35937]
34200ba (4 curves)	1	2+ 3- 5+ 19-	2+ 3- 5+  0  4  2 -2 19-
Curve Equation t Generators 34200ba1 [0,0,0,144825,50188250] 2 [-226:2432:1] 34200ba2 [0,0,0,-1479675,607391750] 4 [16874:2186368:1] 34200ba3 [0,0,0,-6096675,-5177709250] 2 [412949386:53130484352:24389] 34200ba4 [0,0,0,-22854675,42053516750] 2 [509668334:64298889088:29791]
34200bb (2 curves)	1	2+ 3- 5+ 19-	2+ 3- 5+  0  4 -4 -2 19-
Curve Equation t Generators 34200bb1 [0,0,0,-7950,-235375] 2 [-44:171:1] 34200bb2 [0,0,0,13425,-1282750] 2 [431:9196:1]
34200bc (1 curve)	1	2+ 3- 5+ 19-	2+ 3- 5+  2 -5 -2  6 19-
Curve Equation t Generators 34200bc1 [0,0,0,-1875,-981250] 1 [151:1476:1]
34200bd (1 curve)	1	2+ 3- 5+ 19-	2+ 3- 5+  3  1  2 -5 19-
Curve Equation t Generators 34200bd1 [0,0,0,-12900,-641500] 1 [226:2826:1]
34200be (1 curve)	1	2+ 3- 5+ 19-	2+ 3- 5+  3 -6  2  0 19-
Curve Equation t Generators 34200be1 [0,0,0,-255,1555] 1 [11:9:1]
34200bf (1 curve)	1	2+ 3- 5+ 19-	2+ 3- 5+ -3 -2 -1 -5 19-
Curve Equation t Generators 34200bf1 [0,0,0,-1875,44750] 1 [-10:250:1]
34200bg (4 curves)	1	2+ 3- 5+ 19-	2+ 3- 5+ -4  4 -2 -6 19-
Curve Equation t Generators 34200bg1 [0,0,0,-57450,-2413375] 2 [-44:171:1] 34200bg2 [0,0,0,-463575,119830250] 4 [-770:4500:1] 34200bg3 [0,0,0,-36075,332297750] 2 [-694:4804:1] 34200bg4 [0,0,0,-7389075,7730954750] 2 [1510:4050:1]
34200bh (2 curves)	1	2+ 3- 5+ 19-	2+ 3- 5+ -4  4  4  6 19-
Curve Equation t Generators 34200bh1 [0,0,0,-3675,-76250] 2 [71:144:1] 34200bh2 [0,0,0,5325,-391250] 2 [5750:436050:1]
34200bi (2 curves)	1	2+ 3- 5- 19+	2+ 3- 5- -2  4 -6 -4 19+
Curve Equation t Generators 34200bi1 [0,0,0,-23250,565625] 2 [-100:1375:1] 34200bi2 [0,0,0,83625,4306250] 2 [71:3256:1]
34200bj (2 curves)	1	2+ 3- 5- 19+	2+ 3- 5- -2 -4  0  8 19+
Curve Equation t Generators 34200bj1 [0,0,0,-5430,-152575] 2 [-40:25:1] 34200bj2 [0,0,0,-86655,-9818350] 2 [955:27900:1]
34200bk (1 curve)	1	2+ 3- 5- 19+	2+ 3- 5- -3 -4  4  4 19+
Curve Equation t Generators 34200bk1 [0,0,0,-1875,19375] 1 [-25:225:1]
34200bl (2 curves)	1	2+ 3- 5- 19+	2+ 3- 5-  4  0  0 -6 19+
Curve Equation t Generators 34200bl1 [0,0,0,-2235,-43450] 2 [1594:63612:1] 34200bl2 [0,0,0,-36435,-2676850] 2 [43158:1712564:27]
34200bm (2 curves)	1	2+ 3- 5- 19+	2+ 3- 5-  4 -4 -6  2 19+
Curve Equation t Generators 34200bm1 [0,0,0,-2955,82550] 2 [31:144:1] 34200bm2 [0,0,0,-51555,4505150] 2 [-250:1330:1]
34200bn (1 curve)	0	2+ 3- 5- 19-	2+ 3- 5-  1  4  4  6 19-
Curve Equation t 34200bn1 [0,0,0,-17175,-832925] 1
34200bo (2 curves)	0	2+ 3- 5- 19-	2+ 3- 5- -2  4  2  0 19-
Curve Equation t 34200bo1 [0,0,0,59145,-12891350] 2 34200bo2 [0,0,0,-596955,-155265050] 2
34200bp (2 curves)	0	2+ 3- 5- 19-	2+ 3- 5- -2 -4  2  0 19-
Curve Equation t 34200bp1 [0,0,0,-6375,1156250] 2 34200bp2 [0,0,0,-208875,36593750] 2
34200bq (1 curve)	2	2+ 3- 5- 19-	2+ 3- 5- -3 -2 -6  0 19-
Curve Equation t Generators 34200bq1 [0,0,0,-6375,101275] 1 [395:-7695:1]&[-45:545:1]
34200br (1 curve)	0	2+ 3- 5- 19-	2+ 3- 5-  5  0  4  2 19-
Curve Equation t 34200br1 [0,0,0,-28875,-1875625] 1
34200bs (2 curves)	0	2- 3+ 5+ 19+	2- 3+ 5+  0 -2  0  0 19+
Curve Equation t 34200bs1 [0,0,0,-297075,62322750] 2 34200bs2 [0,0,0,-300075,60999750] 2
34200bt (2 curves)	0	2- 3+ 5+ 19+	2- 3+ 5+  0  6 -2  4 19+
Curve Equation t 34200bt1 [0,0,0,-4050,118125] 2 34200bt2 [0,0,0,-68175,6851250] 2
34200bu (1 curve)	0	2- 3+ 5+ 19+	2- 3+ 5+ -1 -2  4  2 19+
Curve Equation t 34200bu1 [0,0,0,-3375,-75465] 1
34200bv (1 curve)	2	2- 3+ 5+ 19+	2- 3+ 5+ -1 -4 -6  0 19+
Curve Equation t Generators 34200bv1 [0,0,0,-135,135] 1 [-11:17:1]&[-6:27:1]
34200bw (2 curves)	0	2- 3+ 5+ 19+	2- 3+ 5+  2  2  0  6 19+
Curve Equation t 34200bw1 [0,0,0,53325,-544853250] 2 34200bw2 [0,0,0,-9693675,-11393264250] 2
34200bx (1 curve)	0	2- 3+ 5+ 19+	2- 3+ 5+  3 -2  0  6 19+
Curve Equation t 34200bx1 [0,0,0,-1875,-28125] 1
34200by (2 curves)	0	2- 3+ 5+ 19+	2- 3+ 5+ -4 -2  4 -4 19+
Curve Equation t 34200by1 [0,0,0,-108675,13776750] 2 34200by2 [0,0,0,-135675,6405750] 2
34200bz (1 curve)	0	2- 3+ 5+ 19+	2- 3+ 5+ -5  4  2  4 19+
Curve Equation t 34200bz1 [0,0,0,-826875,289321875] 1
34200ca (2 curves)	1	2- 3+ 5+ 19-	2- 3+ 5+  0  2  2 -4 19-
Curve Equation t Generators 34200ca1 [0,0,0,-3375,47250] 2 [-35:350:1] 34200ca2 [0,0,0,10125,330750] 2 [19:728:1]
34200cb (1 curve)	1	2- 3+ 5- 19+	2- 3+ 5-  1  2 -4  2 19+
Curve Equation t Generators 34200cb1 [0,0,0,-9375,349375] 1 [50:-75:1]
34200cc (1 curve)	1	2- 3+ 5- 19+	2- 3+ 5-  1  4  6  0 19+
Curve Equation t Generators 34200cc1 [0,0,0,-375,-625] 1 [25:75:1]
34200cd (2 curves)	1	2- 3+ 5- 19+	2- 3+ 5-  2  2 -6 -2 19+
Curve Equation t Generators 34200cd1 [0,0,0,-90,325] 2 [-10:15:1] 34200cd2 [0,0,0,-15,850] 2 [5:-30:1]
34200ce (2 curves)	1	2- 3+ 5- 19+	2- 3+ 5- -2 -2  6 -2 19+
Curve Equation t Generators 34200ce1 [0,0,0,-20250,-1096875] 2 [886:26009:1] 34200ce2 [0,0,0,-3375,-2868750] 2 [169:1178:1]
34200cf (1 curve)	1	2- 3+ 5- 19+	2- 3+ 5- -3  2  0  6 19+
Curve Equation t Generators 34200cf1 [0,0,0,-675,6075] 1 [9:27:1]
34200cg (1 curve)	1	2- 3+ 5- 19+	2- 3+ 5-  5 -4 -2  4 19+
Curve Equation t Generators 34200cg1 [0,0,0,-3675,-85725] 1 [-35:5:1]
34200ch (4 curves)	1	2- 3- 5+ 19+	2- 3- 5+  0  4  6 -6 19+
Curve Equation t Generators 34200ch1 [0,0,0,-450,-70875] 2 [94:847:1] 34200ch2 [0,0,0,-28575,-1842750] 4 [-99:126:1] 34200ch3 [0,0,0,-51075,1464750] 2 [651:15624:1] 34200ch4 [0,0,0,-456075,-118550250] 2 [835:9100:1]
34200ci (6 curves)	1	2- 3- 5+ 19+	2- 3- 5+  0 -4  2  2 19+
Curve Equation t Generators 34200ci1 [0,0,0,68550,14349125] 2 [14:3913:1] 34200ci2 [0,0,0,-634575,166927250] 4 [-419:18954:1] 34200ci3 [0,0,0,-2772075,-1613610250] 2 [3035:133900:1] 34200ci4 [0,0,0,-9747075,11712464750] 4 [3331:127296:1] 34200ci5 [0,0,0,-9342075,12730229750] 2 [1678472:67413177:512] 34200ci6 [0,0,0,-155952075,749609099750] 2 [6970:35100:1]
34200cj (1 curve)	1	2- 3- 5+ 19+	2- 3- 5+  3 -4 -4 -4 19+
Curve Equation t Generators 34200cj1 [0,0,0,-75,155] 1 [1:9:1]
34200ck (4 curves)	1	2- 3- 5+ 19+	2- 3- 5+ -4  0 -2  2 19+
Curve Equation t Generators 34200ck1 [0,0,0,-21450,1209125] 4 [-155:900:1] 34200ck2 [0,0,0,-22575,1075250] 4 [-35:1350:1] 34200ck3 [0,0,0,44925,6272750] 2 [115:3600:1] 34200ck4 [0,0,0,-108075,-12690250] 2 [-149:324:1]
34200cl (1 curve)	0	2- 3- 5+ 19-	2- 3- 5+ -1  4 -4 -6 19-
Curve Equation t 34200cl1 [0,0,0,-429375,-104115625] 1
34200cm (2 curves)	0	2- 3- 5+ 19-	2- 3- 5+  2  4  2  0 19-
Curve Equation t 34200cm1 [0,0,0,5325,26750] 2 34200cm2 [0,0,0,-21675,215750] 2
34200cn (2 curves)	0	2- 3- 5+ 19-	2- 3- 5+ -2  0  2  4 19-
Curve Equation t 34200cn1 [0,0,0,3140925,-1754167250] 2 34200cn2 [0,0,0,-16542075,-15945610250] 2
34200co (2 curves)	2	2- 3- 5+ 19-	2- 3- 5+ -2 -6 -4 -2 19-
Curve Equation t Generators 34200co1 [0,0,0,-4575,225250] 2 [5:-450:1]&[-70:450:1] 34200co2 [0,0,0,-90075,10399750] 2 [-205:4500:1]&[35:2700:1]
34200cp (1 curve)	0	2- 3- 5+ 19-	2- 3- 5+  3 -2  6  0 19-
Curve Equation t 34200cp1 [0,0,0,-159375,12659375] 1
34200cq (1 curve)	0	2- 3- 5+ 19-	2- 3- 5+  3  5  2 -1 19-
Curve Equation t 34200cq1 [0,0,0,12300,-375500] 1
34200cr (1 curve)	2	2- 3- 5+ 19-	2- 3- 5+ -5  0 -4 -2 19-
Curve Equation t Generators 34200cr1 [0,0,0,-1155,-15005] 1 [-19:9:1]&[41:81:1]
34200cs (1 curve)	0	2- 3- 5- 19+	2- 3- 5-  1  0  0 -4 19+
Curve Equation t 34200cs1 [0,0,0,-1113375,437779375] 1
34200ct (1 curve)	0	2- 3- 5- 19+	2- 3- 5-  1 -4 -4  8 19+
Curve Equation t 34200ct1 [0,0,0,-13461375,-19010005625] 1
34200cu (2 curves)	0	2- 3- 5- 19+	2- 3- 5-  2  4  6  4 19+
Curve Equation t 34200cu1 [0,0,0,-930,4525] 2 34200cu2 [0,0,0,3345,34450] 2
34200cv (2 curves)	0	2- 3- 5- 19+	2- 3- 5-  2 -4  0 -8 19+
Curve Equation t 34200cv1 [0,0,0,-135750,-19071875] 2 34200cv2 [0,0,0,-2166375,-1227293750] 2
34200cw (1 curve)	0	2- 3- 5- 19+	2- 3- 5- -2  1  6  6 19+
Curve Equation t 34200cw1 [0,0,0,-136875,-25146250] 1
34200cx (2 curves)	0	2- 3- 5- 19+	2- 3- 5- -4  0  0  6 19+
Curve Equation t 34200cx1 [0,0,0,-55875,-5431250] 2 34200cx2 [0,0,0,-910875,-334606250] 2
34200cy (2 curves)	0	2- 3- 5- 19+	2- 3- 5- -4 -4  6 -2 19+
Curve Equation t 34200cy1 [0,0,0,-73875,10318750] 2 34200cy2 [0,0,0,-1288875,563143750] 2
34200cz (2 curves)	1	2- 3- 5- 19-	2- 3- 5-  2  4 -2  0 19-
Curve Equation t Generators 34200cz1 [0,0,0,1478625,-1611418750] 2 [781:4446:1] 34200cz2 [0,0,0,-14923875,-19408131250] 2 [547531:405137304:1]
34200da (2 curves)	1	2- 3- 5- 19-	2- 3- 5-  2 -4 -2  0 19-
Curve Equation t Generators 34200da1 [0,0,0,-255,9250] 2 [5:-90:1] 34200da2 [0,0,0,-8355,292750] 2 [-45:760:1]
34200db (1 curve)	1	2- 3- 5- 19-	2- 3- 5- -2 -5  2 -6 19-
Curve Equation t Generators 34200db1 [0,0,0,-75,-7850] 1 [35:-180:1]
34200dc (1 curve)	1	2- 3- 5- 19-	2- 3- 5- -3 -6 -2  0 19-
Curve Equation t Generators 34200dc1 [0,0,0,-6375,194375] 1 [25:-225:1]

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