Cremona's table of elliptic curves

82170 = 2 · 3² · 5 · 11 · 83

Class	r	Atkin-Lehner	Eigenvalues
82170a (1 curve)	1	2+ 3+ 5+ 11+ 83+	2+ 3+ 5+  1 11+ -3  2  2
Curve Equation t Generators 82170a1 [1,-1,0,-5730,-168300] 1 [6132:22161:64]
82170b (2 curves)	0	2+ 3+ 5+ 11+ 83-	2+ 3+ 5+ -1 11+  5  6  2
Curve Equation t 82170b1 [1,-1,0,-510,4986] 3 82170b2 [1,-1,0,3225,-8875] 1
82170c (2 curves)	1	2+ 3+ 5+ 11- 83-	2+ 3+ 5+ -4 11- -1  0 -7
Curve Equation t Generators 82170c1 [1,-1,0,-117660,15557616] 3 [-90:32913:8] 82170c2 [1,-1,0,-350475,-60866875] 1 [-1594:8897:8]
82170d (2 curves)	0	2+ 3+ 5- 11+ 83+	2+ 3+ 5-  0 11+ -4  8 -2
Curve Equation t 82170d1 [1,-1,0,-15684,-752112] 2 82170d2 [1,-1,0,-15564,-764280] 2
82170e (1 curve)	1	2+ 3+ 5- 11+ 83-	2+ 3+ 5-  0 11+ -5  0  1
Curve Equation t Generators 82170e1 [1,-1,0,-54,110] 1 [1:7:1]
82170f (2 curves)	1	2+ 3+ 5- 11+ 83-	2+ 3+ 5- -4 11+  2 -4  6
Curve Equation t Generators 82170f1 [1,-1,0,-9249,212093] 2 [-53:769:1] 82170f2 [1,-1,0,-63249,-5954707] 2 [-133:369:1]
82170g (1 curve)	2	2+ 3- 5+ 11+ 83+	2+ 3- 5+  1 11+ -3  2 -4
Curve Equation t Generators 82170g1 [1,-1,0,45,9801] 1 [-18:63:1]&[-17:71:1]
82170h (1 curve)	2	2+ 3- 5+ 11+ 83+	2+ 3- 5+  1 11+ -5  0 -4
Curve Equation t Generators 82170h1 [1,-1,0,-592470,-251893004] 1 [1340:36194:1]&[1743:62441:1]
82170i (2 curves)	0	2+ 3- 5+ 11+ 83+	2+ 3- 5+  2 11+  2  2 -4
Curve Equation t 82170i1 [1,-1,0,540,734800] 2 82170i2 [1,-1,0,-118980,15531376] 2
82170j (2 curves)	1	2+ 3- 5+ 11+ 83-	2+ 3- 5+  0 11+  2 -2  6
Curve Equation t Generators 82170j1 [1,-1,0,750,-15904] 2 [241:3637:1] 82170j2 [1,-1,0,-6720,-178750] 2 [-35:130:1]
82170k (1 curve)	1	2+ 3- 5+ 11+ 83-	2+ 3- 5+  0 11+  7  3  1
Curve Equation t Generators 82170k1 [1,-1,0,-12115635,16234855541] 1 [-203:136798:1]
82170l (1 curve)	1	2+ 3- 5+ 11+ 83-	2+ 3- 5+ -2 11+  3 -2  7
Curve Equation t Generators 82170l1 [1,-1,0,-211680,37534720] 1 [263:-82:1]
82170m (1 curve)	1	2+ 3- 5+ 11+ 83-	2+ 3- 5+  4 11+  6 -2 -2
Curve Equation t Generators 82170m1 [1,-1,0,45,121] 1 [0:11:1]
82170n (1 curve)	1	2+ 3- 5+ 11+ 83-	2+ 3- 5+ -4 11+ -1 -5 -5
Curve Equation t Generators 82170n1 [1,-1,0,45,-2457675] 1 [141:510:1]
82170o (1 curve)	1	2+ 3- 5+ 11- 83+	2+ 3- 5+ -1 11-  1  0 -6
Curve Equation t Generators 82170o1 [1,-1,0,-684765,241377925] 1 [503:4649:1]
82170p (1 curve)	1	2+ 3- 5+ 11- 83+	2+ 3- 5+  2 11-  1 -7  3
Curve Equation t Generators 82170p1 [1,-1,0,-900,10786] 1 [17:5:1]
82170q (1 curve)	0	2+ 3- 5+ 11- 83-	2+ 3- 5+  2 11-  1  4  1
Curve Equation t 82170q1 [1,-1,0,-495,2605] 1
82170r (4 curves)	0	2+ 3- 5+ 11- 83-	2+ 3- 5+  2 11-  2 -6  2
Curve Equation t 82170r1 [1,-1,0,-997605,-364365675] 2 82170r2 [1,-1,0,-2909925,1451955861] 2 82170r3 [1,-1,0,-13741605,19520032725] 6 82170r4 [1,-1,0,-219584925,1252480350861] 6
82170s (1 curve)	0	2+ 3- 5+ 11- 83-	2+ 3- 5+  2 11-  5 -2  1
Curve Equation t 82170s1 [1,-1,0,-370665,-86452569] 1
82170t (2 curves)	1	2+ 3- 5- 11+ 83+	2+ 3- 5-  0 11+  2  2 -2
Curve Equation t Generators 82170t1 [1,-1,0,5526,68148] 2 [1509:57921:1] 82170t2 [1,-1,0,-24354,588060] 2 [21:282:1]
82170u (2 curves)	1	2+ 3- 5- 11+ 83+	2+ 3- 5-  0 11+  6  0  8
Curve Equation t Generators 82170u1 [1,-1,0,-54,1188] 2 [4:30:1] 82170u2 [1,-1,0,-2034,35640] 2 [4:164:1]
82170v (1 curve)	1	2+ 3- 5- 11+ 83+	2+ 3- 5-  1 11+  7  0  2
Curve Equation t Generators 82170v1 [1,-1,0,-91584,-10645160] 1 [509:8372:1]
82170w (1 curve)	1	2+ 3- 5- 11+ 83+	2+ 3- 5- -3 11+ -7  2 -8
Curve Equation t Generators 82170w1 [1,-1,0,67536,-10126080] 1 [480:11280:1]
82170x (2 curves)	0	2+ 3- 5- 11+ 83-	2+ 3- 5-  2 11+  5  6  5
Curve Equation t 82170x1 [1,-1,0,-1494,-16740] 1 82170x2 [1,-1,0,-40104,3099978] 3
82170y (1 curve)	0	2+ 3- 5- 11- 83+	2+ 3- 5-  3 11-  1  0 -2
Curve Equation t 82170y1 [1,-1,0,203436,39836880] 1
82170z (2 curves)	1	2+ 3- 5- 11- 83-	2+ 3- 5- -1 11- -1  0  8
Curve Equation t Generators 82170z1 [1,-1,0,81666,1755540] 1 [204:5082:1] 82170z2 [1,-1,0,-1259694,567891108] 3 [672:4614:1]
82170ba (1 curve)	1	2+ 3- 5- 11- 83-	2+ 3- 5-  2 11-  1  7 -1
Curve Equation t Generators 82170ba1 [1,-1,0,4851,138213] 1 [8445:105528:125]
82170bb (1 curve)	1	2+ 3- 5- 11- 83-	2+ 3- 5-  2 11-  3 -8  1
Curve Equation t Generators 82170bb1 [1,-1,0,-19089,-1005755] 1 [-79:107:1]
82170bc (1 curve)	1	2+ 3- 5- 11- 83-	2+ 3- 5- -2 11-  7  0  3
Curve Equation t Generators 82170bc1 [1,-1,0,-155349,-9699345] 1 [-219:3822:1]
82170bd (2 curves)	1	2+ 3- 5- 11- 83-	2+ 3- 5-  4 11- -2  0  0
Curve Equation t Generators 82170bd1 [1,-1,0,-66704229,209702504853] 2 [8667:527229:1] 82170bd2 [1,-1,0,-64215909,226067190165] 2 [-4239:651807:1]
82170be (4 curves)	1	2+ 3- 5- 11- 83-	2+ 3- 5- -4 11- -2 -2 -4
Curve Equation t Generators 82170be1 [1,-1,0,-107964,-13623552] 2 [-188:144:1] 82170be2 [1,-1,0,-122544,-9695700] 4 [591:-11433:1] 82170be3 [1,-1,0,383706,-69534450] 2 [231:5487:1] 82170be4 [1,-1,0,-862074,301350618] 2 [757:8684:1]
82170bf (4 curves)	1	2+ 3- 5- 11- 83-	2+ 3- 5- -4 11-  6 -2  4
Curve Equation t Generators 82170bf1 [1,-1,0,-824949,243825205] 2 [995:19685:1] 82170bf2 [1,-1,0,-12621429,17261427253] 4 [2123:4541:1] 82170bf3 [1,-1,0,-12045429,18907750453] 2 [959:90281:1] 82170bf4 [1,-1,0,-201941109,1104600077365] 2 [233247:1738064:27]
82170bg (1 curve)	1	2+ 3- 5- 11- 83-	2+ 3- 5- -5 11-  1  6  0
Curve Equation t Generators 82170bg1 [1,-1,0,-1899,-31995] 1 [54:117:1]
82170bh (1 curve)	1	2- 3+ 5+ 11- 83+	2- 3+ 5+  0 11- -5  0  1
Curve Equation t Generators 82170bh1 [1,-1,1,-488,-2483] 1 [-812:2885:64]
82170bi (2 curves)	1	2- 3+ 5+ 11- 83+	2- 3+ 5+ -4 11-  2  4  6
Curve Equation t Generators 82170bi1 [1,-1,1,-1028,-7513] 2 [-15:73:1] 82170bi2 [1,-1,1,-7028,222887] 2 [283:-4707:1]
82170bj (2 curves)	2	2- 3+ 5+ 11- 83-	2- 3+ 5+  0 11- -4 -8 -2
Curve Equation t Generators 82170bj1 [1,-1,1,-141158,20448181] 2 [-269:6371:1]&[-25:4907:1] 82170bj2 [1,-1,1,-140078,20775637] 2 [-205:6493:1]&[127:2177:1]
82170bk (2 curves)	1	2- 3+ 5- 11+ 83+	2- 3+ 5- -4 11+ -1  0 -7
Curve Equation t Generators 82170bk1 [1,-1,1,-38942,2267309] 3 [-183:1891:1] 82170bk2 [1,-1,1,-1058942,-418996691] 1 [-593:701:1]
82170bl (2 curves)	0	2- 3+ 5- 11- 83+	2- 3+ 5- -1 11-  5 -6  2
Curve Equation t 82170bl1 [1,-1,1,358,209] 3 82170bl2 [1,-1,1,-4592,-130031] 1
82170bm (1 curve)	1	2- 3+ 5- 11- 83-	2- 3+ 5-  1 11- -3 -2  2
Curve Equation t Generators 82170bm1 [1,-1,1,-51572,4595671] 1 [181:989:1]
82170bn (1 curve)	1	2- 3- 5+ 11+ 83+	2- 3- 5+  2 11+ -1  2  3
Curve Equation t Generators 82170bn1 [1,-1,1,-99158,12026981] 1 [153:-725:1]
82170bo (1 curve)	1	2- 3- 5+ 11+ 83+	2- 3- 5+ -2 11+ -1  4  1
Curve Equation t Generators 82170bo1 [1,-1,1,-558068,152426711] 1 [141:8677:1]
82170bp (2 curves)	1	2- 3- 5+ 11+ 83+	2- 3- 5+ -2 11+  2 -2 -2
Curve Equation t Generators 82170bp1 [1,-1,1,-653,-1519] 2 [-5:42:1] 82170bp2 [1,-1,1,-8123,-279403] 2 [1950:26939:8]
82170bq (2 curves)	1	2- 3- 5+ 11+ 83+	2- 3- 5+  4 11+ -2 -6 -6
Curve Equation t Generators 82170bq1 [1,-1,1,-5648,418547] 2 [45:481:1] 82170bq2 [1,-1,1,-125168,17055731] 2 [105:2197:1]
82170br (4 curves)	0	2- 3- 5+ 11+ 83-	2- 3- 5+ -4 11+  2  0 -4
Curve Equation t 82170br1 [1,-1,1,-61943,-6553393] 2 82170br2 [1,-1,1,-1020263,-396397969] 2 82170br3 [1,-1,1,400882,15694877] 6 82170br4 [1,-1,1,-1626638,127613981] 6
82170bs (1 curve)	0	2- 3- 5+ 11- 83+	2- 3- 5+  0 11-  6  6 -2
Curve Equation t 82170bs1 [1,-1,1,-418808,-104216453] 1
82170bt (2 curves)	1	2- 3- 5+ 11- 83-	2- 3- 5+  0 11-  0  6 -4
Curve Equation t Generators 82170bt1 [1,-1,1,-48443,-4055893] 2 [-135:166:1] 82170bt2 [1,-1,1,-12443,-9974293] 2 [463:-9362:1]
82170bu (1 curve)	1	2- 3- 5+ 11- 83-	2- 3- 5+  2 11-  7 -5 -5
Curve Equation t Generators 82170bu1 [1,-1,1,-27878,-1848459] 1 [281:3387:1]
82170bv (2 curves)	1	2- 3- 5+ 11- 83-	2- 3- 5+ -2 11- -6  2  6
Curve Equation t Generators 82170bv1 [1,-1,1,-35303,2560187] 2 [-177:1888:1] 82170bv2 [1,-1,1,-42773,1403831] 2 [19614:957815:8]
82170bw (1 curve)	0	2- 3- 5- 11+ 83+	2- 3- 5-  0 11+  2  2 -2
Curve Equation t 82170bw1 [1,-1,1,484753,-590643529] 1
82170bx (2 curves)	0	2- 3- 5- 11+ 83+	2- 3- 5-  0 11+ -6  0  4
Curve Equation t 82170bx1 [1,-1,1,-12945767,-17925091041] 2 82170bx2 [1,-1,1,-12941447,-17937655329] 2
82170by (4 curves)	0	2- 3- 5- 11+ 83+	2- 3- 5- -4 11+  2 -2  8
Curve Equation t 82170by1 [1,-1,1,262003,104079269] 2 82170by2 [1,-1,1,-2373377,1201451501] 4 82170by3 [1,-1,1,-10508207,-11947687711] 2 82170by4 [1,-1,1,-36404627,84550789001] 2
82170bz (1 curve)	1	2- 3- 5- 11- 83+	2- 3- 5-  1 11- -6 -1  7
Curve Equation t Generators 82170bz1 [1,-1,1,-81977,28839129] 1 [117:4506:1]
82170ca (1 curve)	1	2- 3- 5- 11- 83+	2- 3- 5-  2 11- -1  2 -1
Curve Equation t Generators 82170ca1 [1,-1,1,-3636942467,-84292714342141] 1 [-34233:320866:1]
82170cb (2 curves)	1	2- 3- 5- 11- 83+	2- 3- 5-  2 11- -1 -3 -1
Curve Equation t Generators 82170cb1 [1,-1,1,39433,517529] 1 [92190:2173777:1000] 82170cb2 [1,-1,1,-599252,186838751] 3 [-3882:154397:8]
82170cc (4 curves)	1	2- 3- 5- 11- 83+	2- 3- 5- -4 11-  2  2 -4
Curve Equation t Generators 82170cc1 [1,-1,1,-4712,122411] 2 [-9:409:1] 82170cc2 [1,-1,1,-11192,-281941] 4 [-81:337:1] 82170cc3 [1,-1,1,33628,-2003029] 4 [85:1167:1] 82170cc4 [1,-1,1,-159692,-24517141] 2 [-231:187:1]
82170cd (1 curve)	1	2- 3- 5- 11- 83+	2- 3- 5- -5 11-  3 -4 -2
Curve Equation t Generators 82170cd1 [1,-1,1,-167,2751] 1 [-1:54:1]

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