Cremona's table of elliptic curves

100050 = 2 · 3 · 5² · 23 · 29

Class	r	Atkin-Lehner	Eigenvalues
100050a (1 curve)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+  0  2  3  6 -7
Curve Equation t Generators 100050a1 [1,1,0,-25875,-1612875] 1 [124889:44073060:1]
100050b (2 curves)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+  0 -4  0  0 -4
Curve Equation t Generators 100050b1 [1,1,0,-993375,437653125] 2 [15285:196420:27] 100050b2 [1,1,0,-16545375,25896277125] 2 [2665:25855:1]
100050c (4 curves)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+ -2  0 -2 -6  2
Curve Equation t Generators 100050c1 [1,1,0,106225,15985125] 2 [86:5033:1] 100050c2 [1,1,0,-676775,157708125] 2 [811:11556:1] 100050c3 [1,1,0,-1032275,-664734375] 2 [72536:19497731:1] 100050c4 [1,1,0,-19324025,-32693588625] 2 [94002683569:25231882278024:1295029]
100050d (2 curves)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+ -2 -2  4  2 -4
Curve Equation t Generators 100050d1 [1,1,0,-105114625,151647227125] 2 [-127020:38058935:64] 100050d2 [1,1,0,-1364826625,19391228603125] 2 [8106927515700:-400680613228225:308915776]
100050e (1 curve)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+  4 -2  1  2  5
Curve Equation t Generators 100050e1 [1,1,0,-64875,8128125] 1 [1558:12909:8]
100050f (2 curves)	1	2+ 3+ 5+ 23+ 29+	2+ 3+ 5+  4 -2 -2  0 -2
Curve Equation t Generators 100050f1 [1,1,0,-398375,-241996875] 2 [11109275530:768306114235:2248091] 100050f2 [1,1,0,-8750375,-9955372875] 2 [19790:2741105:1]
100050g (1 curve)	0	2+ 3+ 5+ 23+ 29-	2+ 3+ 5+  0 -3  5  4  4
Curve Equation t 100050g1 [1,1,0,-33150,-11119500] 1
100050h (1 curve)	0	2+ 3+ 5+ 23+ 29-	2+ 3+ 5+  3  0  2 -5 -5
Curve Equation t 100050h1 [1,1,0,-692650,234140500] 1
100050i (4 curves)	2	2+ 3+ 5+ 23+ 29-	2+ 3+ 5+ -4  0 -2 -2 -4
Curve Equation t Generators 100050i1 [1,1,0,-44750,3496500] 2 [-1922:6343:8]&[-180:2490:1] 100050i2 [1,1,0,-116750,-10687500] 4 [-245:1935:1]&[-225:2175:1] 100050i3 [1,1,0,318250,-71152500] 2 [355:9135:1]&[471:13311:1] 100050i4 [1,1,0,-1703750,-856558500] 2 [-749:623:1]&[12470:127165:8]
100050j (2 curves)	0	2+ 3+ 5+ 23- 29+	2+ 3+ 5+ -2  0  1  6 -1
Curve Equation t 100050j1 [1,1,0,1174350,-3988327500] 1 100050j2 [1,1,0,-158476650,-768189550500] 1
100050k (2 curves)	0	2+ 3+ 5+ 23- 29+	2+ 3+ 5+  4  3 -5  6  2
Curve Equation t 100050k1 [1,1,0,-2300,42000] 1 100050k2 [1,1,0,8200,220500] 1
100050l (1 curve)	1	2+ 3+ 5+ 23- 29-	2+ 3+ 5+ -1  0  2 -1 -1
Curve Equation t Generators 100050l1 [1,1,0,-45280600,117259087000] 1 [3291:60788:1]
100050m (4 curves)	1	2+ 3+ 5+ 23- 29-	2+ 3+ 5+  4  0  2 -6  4
Curve Equation t Generators 100050m1 [1,1,0,-14225,-2530875] 2 [121485:2026170:343] 100050m2 [1,1,0,-378725,-89646375] 4 [1435:47495:1] 100050m3 [1,1,0,-533975,-9382125] 2 [784693:35168918:343] 100050m4 [1,1,0,-6055475,-5738012625] 2 [3001:54426:1]
100050n (2 curves)	1	2+ 3+ 5+ 23- 29-	2+ 3+ 5+ -4  0  2 -4  8
Curve Equation t Generators 100050n1 [1,1,0,-1825,-36875] 2 [79:526:1] 100050n2 [1,1,0,-30825,-2095875] 2 [279:3195:1]
100050o (2 curves)	0	2+ 3+ 5- 23+ 29+	2+ 3+ 5-  2  2  1  2  5
Curve Equation t 100050o1 [1,1,0,43675,-656625] 1 100050o2 [1,1,0,-4288200,3417084000] 1
100050p (2 curves)	0	2+ 3+ 5- 23+ 29+	2+ 3+ 5-  2 -3  1 -3 -5
Curve Equation t 100050p1 [1,1,0,-1660750,-824459600] 1 100050p2 [1,1,0,1067425,-3165802875] 1
100050q (2 curves)	0	2+ 3+ 5- 23+ 29+	2+ 3+ 5-  4 -2  4  6 -2
Curve Equation t 100050q1 [1,1,0,-2553325,977732125] 2 100050q2 [1,1,0,7686675,6865732125] 2
100050r (1 curve)	1	2+ 3+ 5- 23- 29+	2+ 3+ 5-  0 -4  7  6 -5
Curve Equation t Generators 100050r1 [1,1,0,7550,176500] 1 [39:710:1]
100050s (1 curve)	1	2+ 3+ 5- 23- 29+	2+ 3+ 5-  2  0 -2 -2 -6
Curve Equation t Generators 100050s1 [1,1,0,-155575,25247125] 1 [361:3856:1]
100050t (4 curves)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+  0  0  6  6 -4
Curve Equation t 100050t1 [1,0,1,275624,9879279398] 2 100050t2 [1,0,1,-67436376,209223407398] 4 100050t3 [1,0,1,-144808376,-360234512602] 2 100050t4 [1,0,1,-1073456376,13536976367398] 2
100050u (1 curve)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+ -1 -4  2  3  1
Curve Equation t 100050u1 [1,0,1,1624,-14602] 1
100050v (2 curves)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+  2  2  2  0  4
Curve Equation t 100050v1 [1,0,1,-135726,-24189152] 2 100050v2 [1,0,1,-2322726,-1362633152] 2
100050w (2 curves)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+  2  6 -2  0  0
Curve Equation t 100050w1 [1,0,1,-672501,-212644352] 2 100050w2 [1,0,1,-10764501,-13594636352] 2
100050x (2 curves)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+ -2  2 -2 -4  8
Curve Equation t 100050x1 [1,0,1,116374,-6819352] 2 100050x2 [1,0,1,-514376,-57279352] 2
100050y (2 curves)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+ -2 -2  2 -4 -4
Curve Equation t 100050y1 [1,0,1,-2726,-1286152] 2 100050y2 [1,0,1,-194726,-32774152] 2
100050z (1 curve)	0	2+ 3- 5+ 23+ 29+	2+ 3- 5+  4  1 -1  2  2
Curve Equation t 100050z1 [1,0,1,43374,30546148] 1
100050ba (2 curves)	2	2+ 3- 5+ 23+ 29+	2+ 3- 5+ -4 -6 -2  0  0
Curve Equation t Generators 100050ba1 [1,0,1,-84251,9405398] 2 [147:376:1]&[-78:3976:1] 100050ba2 [1,0,1,-81751,9990398] 2 [-8:-3259:1]&[-233:4166:1]
100050bb (4 curves)	1	2+ 3- 5+ 23+ 29-	2+ 3- 5+ -4  0  2  6  4
Curve Equation t Generators 100050bb1 [1,0,1,-1176,-15002] 2 [121:1211:1] 100050bb2 [1,0,1,-3176,48998] 4 [12:106:1] 100050bb3 [1,0,1,8324,324998] 2 [31:767:1] 100050bb4 [1,0,1,-46676,3876998] 2 [128:-3:1]
100050bc (4 curves)	1	2+ 3- 5+ 23+ 29-	2+ 3- 5+ -4  4 -6  2  4
Curve Equation t Generators 100050bc1 [1,0,1,-45510026,-118036530052] 2 [-26019702:-16477016:6859] 100050bc2 [1,0,1,-58310026,-46305330052] 4 [-4178:354776:1] 100050bc3 [1,0,1,223569974,-363138450052] 2 [12526:2091992:1] 100050bc4 [1,0,1,-544990026,4861375789948] 4 [-13978:3129201:1]
100050bd (1 curve)	1	2+ 3- 5+ 23- 29+	2+ 3- 5+  2 -3 -5  3 -1
Curve Equation t Generators 100050bd1 [1,0,1,78424,53015798] 1 [-279:3211:1]
100050be (1 curve)	1	2+ 3- 5+ 23- 29+	2+ 3- 5+ -2 -1 -5 -7 -7
Curve Equation t Generators 100050be1 [1,0,1,-351,2638] 1 [-7:72:1]
100050bf (1 curve)	0	2+ 3- 5+ 23- 29-	2+ 3- 5+  3  0 -6 -2 -3
Curve Equation t 100050bf1 [1,0,1,-36,-452] 1
100050bg (1 curve)	2	2+ 3- 5+ 23- 29-	2+ 3- 5+ -4 -2 -3  2 -5
Curve Equation t Generators 100050bg1 [1,0,1,14224,9488198] 1 [-168:1621:1]&[-108:2641:1]
100050bh (1 curve)	0	2+ 3- 5- 23+ 29-	2+ 3- 5-  1  0  2  6 -1
Curve Equation t 100050bh1 [1,0,1,-7865801,-8569281652] 1
100050bi (2 curves)	0	2+ 3- 5- 23- 29+	2+ 3- 5-  0  2  0  6  6
Curve Equation t 100050bi1 [1,0,1,-33951,-2090702] 2 100050bi2 [1,0,1,56049,-11270702] 2
100050bj (2 curves)	0	2+ 3- 5- 23- 29+	2+ 3- 5-  2  0  4 -2 -4
Curve Equation t 100050bj1 [1,0,1,43799,-1202452] 2 100050bj2 [1,0,1,-186201,-9942452] 2
100050bk (2 curves)	0	2- 3+ 5+ 23+ 29+	2- 3+ 5+  0  2  6  0 -4
Curve Equation t 100050bk1 [1,1,1,-693088,214065281] 2 100050bk2 [1,1,1,306912,782065281] 2
100050bl (2 curves)	0	2- 3+ 5+ 23+ 29+	2- 3+ 5+  0  2  6  8 -2
Curve Equation t 100050bl1 [1,1,1,-306863,69889781] 2 100050bl2 [1,1,1,-5004863,4307485781] 2
100050bm (1 curve)	0	2- 3+ 5+ 23+ 29+	2- 3+ 5+  3  2  0 -3 -1
Curve Equation t 100050bm1 [1,1,1,-11113,454031] 1
100050bn (4 curves)	0	2- 3+ 5+ 23+ 29+	2- 3+ 5+  4 -4  2  2  4
Curve Equation t 100050bn1 [1,1,1,-22713,-270969] 2 100050bn2 [1,1,1,-222713,40129031] 4 100050bn3 [1,1,1,-87713,88459031] 2 100050bn4 [1,1,1,-3557713,2581399031] 2
100050bo (2 curves)	0	2- 3+ 5+ 23+ 29+	2- 3+ 5+  4 -6 -2  0 -6
Curve Equation t 100050bo1 [1,1,1,-1213,-753469] 2 100050bo2 [1,1,1,-131713,-18240469] 2
100050bp (1 curve)	1	2- 3+ 5+ 23+ 29-	2- 3+ 5+  0 -2 -1 -2  3
Curve Equation t Generators 100050bp1 [1,1,1,412562,-390960469] 1 [1489:-60137:1]
100050bq (2 curves)	1	2- 3+ 5+ 23- 29+	2- 3+ 5+  0  0  2 -4  4
Curve Equation t Generators 100050bq1 [1,1,1,-352338,-80654469] 2 [383465669433435:17034372818847447:174770640071] 100050bq2 [1,1,1,-5637588,-5154494469] 2 [14660346907954850257089668916:260170845913336962472195251135:5064801784462874138660416]
100050br (1 curve)	1	2- 3+ 5+ 23- 29+	2- 3+ 5+  0  5 -3 -4  4
Curve Equation t Generators 100050br1 [1,1,1,-17463,1808781] 1 [-21:1482:1]
100050bs (4 curves)	0	2- 3+ 5+ 23- 29-	2- 3+ 5+  0 -4 -6 -2 -4
Curve Equation t 100050bs1 [1,1,1,4885738062,-135512744043969] 2 100050bs2 [1,1,1,-28668693938,-1294214389867969] 4 100050bs3 [1,1,1,-175868693938,27386822410132031] 2 100050bs4 [1,1,1,-418339605938,-104131485433963969] 2
100050bt (1 curve)	0	2- 3+ 5+ 23- 29-	2- 3+ 5+ -1  0 -2 -6 -1
Curve Equation t 100050bt1 [1,1,1,-196645013,-1071160206469] 1
100050bu (2 curves)	0	2- 3+ 5+ 23- 29-	2- 3+ 5+  2  6 -4  2 -4
Curve Equation t 100050bu1 [1,1,1,-1014963,392815281] 2 100050bu2 [1,1,1,-1257963,190153281] 2
100050bv (2 curves)	2	2- 3+ 5+ 23- 29-	2- 3+ 5+ -2  0 -5 -6 -7
Curve Equation t Generators 100050bv1 [1,1,1,-19588,1087781] 1 [-161:397:1]&[-95:1497:1] 100050bv2 [1,1,1,100037,2958281] 1 [-29:198:1]&[115:-4058:1]
100050bw (2 curves)	0	2- 3+ 5+ 23- 29-	2- 3+ 5+ -4  0  4  0 -4
Curve Equation t 100050bw1 [1,1,1,1287,6531] 2 100050bw2 [1,1,1,-5463,47031] 2
100050bx (2 curves)	1	2- 3+ 5- 23+ 29+	2- 3+ 5-  0  2  0 -6  6
Curve Equation t Generators 100050bx1 [1,1,1,-1358,-17269] 2 [-19:55:1] 100050bx2 [1,1,1,2242,-89269] 2 [65:-613:1]
100050by (1 curve)	1	2- 3+ 5- 23+ 29+	2- 3+ 5-  2 -1  5  7 -7
Curve Equation t Generators 100050by1 [1,1,1,-8763,329781] 1 [79:332:1]
100050bz (2 curves)	1	2- 3+ 5- 23+ 29+	2- 3+ 5- -2  0 -4  2 -4
Curve Equation t Generators 100050bz1 [1,1,1,1752,-8919] 2 [15:137:1] 100050bz2 [1,1,1,-7448,-82519] 2 [-45:427:1]
100050ca (1 curve)	1	2- 3+ 5- 23+ 29+	2- 3+ 5- -2 -3  5 -3 -1
Curve Equation t Generators 100050ca1 [1,1,1,3137,425381] 1 [155:-2238:1]
100050cb (1 curve)	0	2- 3+ 5- 23+ 29-	2- 3+ 5- -3  0  6  2 -3
Curve Equation t 100050cb1 [1,1,1,-888,-56469] 1
100050cc (2 curves)	1	2- 3- 5+ 23+ 29+	2- 3- 5+  2 -4  2  6 -2
Curve Equation t Generators 100050cc1 [1,0,0,-5788,170192] 2 [28:160:1] 100050cc2 [1,0,0,-92788,10871192] 2 [178:-38:1]
100050cd (1 curve)	1	2- 3- 5+ 23+ 29+	2- 3- 5+ -2  0 -1  2 -1
Curve Equation t Generators 100050cd1 [1,0,0,-63,867] 1 [-26:271:8]
100050ce (2 curves)	1	2- 3- 5+ 23+ 29+	2- 3- 5+ -2  0  2  2  6
Curve Equation t Generators 100050ce1 [1,0,0,-5563,-1140883] 2 [2522:125339:1] 100050ce2 [1,0,0,-201313,-34614133] 2 [162452:7966103:64]
100050cf (1 curve)	1	2- 3- 5+ 23+ 29+	2- 3- 5+ -2  0  2  2 -6
Curve Equation t Generators 100050cf1 [1,0,0,-6223,201977] 1 [86:509:1]
100050cg (1 curve)	1	2- 3- 5+ 23+ 29+	2- 3- 5+ -2  0 -5  2 -1
Curve Equation t Generators 100050cg1 [1,0,0,-274020353813,55210562018539617] 1 [302226:-151881:1]
100050ch (2 curves)	1	2- 3- 5+ 23+ 29+	2- 3- 5+  4  0  4 -4 -4
Curve Equation t Generators 100050ch1 [1,0,0,937,-31383] 2 [76:655:1] 100050ch2 [1,0,0,-11063,-403383] 2 [282:4209:1]
100050ci (2 curves)	0	2- 3- 5+ 23- 29+	2- 3- 5+ -2 -3 -1  3 -5
Curve Equation t 100050ci1 [1,0,0,42697,-25326423] 5 100050ci2 [1,0,0,-41518763,-102974412483] 1
100050cj (2 curves)	0	2- 3- 5+ 23- 29+	2- 3- 5+ -2  6  0 -6  0
Curve Equation t 100050cj1 [1,0,0,-999563,-384730383] 2 100050cj2 [1,0,0,-1011563,-375022383] 2
100050ck (2 curves)	0	2- 3- 5+ 23- 29+	2- 3- 5+  4  0 -6  0  0
Curve Equation t 100050ck1 [1,0,0,487,14517] 2 100050ck2 [1,0,0,-6763,195767] 2
100050cl (1 curve)	2	2- 3- 5+ 23- 29+	2- 3- 5+ -4 -6  1 -6 -7
Curve Equation t Generators 100050cl1 [1,0,0,-679838,215876292] 1 [1372:42514:1]&[472:-686:1]
100050cm (2 curves)	1	2- 3- 5+ 23- 29-	2- 3- 5+  2 -2  6 -4  4
Curve Equation t Generators 100050cm1 [1,0,0,66879787,736427496417] 2 [-5102:514807:1] 100050cm2 [1,0,0,-928448213,9986010600417] 2 [12442:594079:1]
100050cn (1 curve)	1	2- 3- 5+ 23- 29-	2- 3- 5+ -4 -3 -1 -6  6
Curve Equation t Generators 100050cn1 [1,0,0,-165313,-26160883] 1 [698:13745:1]
100050co (1 curve)	2	2- 3- 5- 23+ 29+	2- 3- 5-  0 -4 -7 -6 -5
Curve Equation t Generators 100050co1 [1,0,0,302,1412] 1 [2:-46:1]&[-4:14:1]
100050cp (2 curves)	1	2- 3- 5- 23- 29+	2- 3- 5- -2  2 -1 -2  5
Curve Equation t Generators 100050cp1 [1,0,0,1747,-5253] 1 [758550:8959131:125000] 100050cp2 [1,0,0,-171528,27336672] 5 [-444:4224:1]
100050cq (2 curves)	1	2- 3- 5- 23- 29+	2- 3- 5- -4 -2 -4 -6 -2
Curve Equation t Generators 100050cq1 [1,0,0,-102133,7821857] 2 [2:2759:1] 100050cq2 [1,0,0,307467,54925857] 2 [-78:5559:1]

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