Cremona's table of elliptic curves

80586 = 2 · 3² · 11² · 37

Class	r	Atkin-Lehner	Eigenvalues
80586a (2 curves)	0	2+ 3+ 11- 37+	2+ 3+ -2  0 11-  2  2 -2
Curve Equation t 80586a1 [1,-1,0,25932,-153889840] 2 80586a2 [1,-1,0,-4155828,-3195702064] 2
80586b (1 curve)	1	2+ 3+ 11- 37-	2+ 3+ -2  3 11-  3  3 -5
Curve Equation t Generators 80586b1 [1,-1,0,-3108,-66896] 1 [5134:126907:8]
80586c (1 curve)	0	2+ 3- 11+ 37+	2+ 3-  1 -4 11+ -4  5  2
Curve Equation t 80586c1 [1,-1,0,-864,-27648] 1
80586d (1 curve)	0	2+ 3- 11+ 37+	2+ 3- -1 -2 11+  6  1 -8
Curve Equation t 80586d1 [1,-1,0,-4725,-140211] 1
80586e (2 curves)	0	2+ 3- 11+ 37+	2+ 3-  2 -2 11+  0 -2 -2
Curve Equation t 80586e1 [1,-1,0,-769401,-23054355] 2 80586e2 [1,-1,0,3063879,-186352083] 2
80586f (1 curve)	0	2+ 3- 11+ 37+	2+ 3- -3  0 11+  0 -3  6
Curve Equation t 80586f1 [1,-1,0,-9334386,10979232556] 1
80586g (2 curves)	0	2+ 3- 11+ 37+	2+ 3-  4  2 11+  2  2  8
Curve Equation t 80586g1 [1,-1,0,-422010,113470308] 2 80586g2 [1,-1,0,-6890670,6963781248] 2
80586h (2 curves)	1	2+ 3- 11+ 37-	2+ 3-  0 -4 11+ -2 -2 -6
Curve Equation t Generators 80586h1 [1,-1,0,-11478627,-12599668031] 2 [-1708:45809:1] 80586h2 [1,-1,0,-175471137,-894584185313] 2 [17273:1099421:1]
80586i (2 curves)	1	2+ 3- 11+ 37-	2+ 3- -2 -4 11+  4 -2  8
Curve Equation t Generators 80586i1 [1,-1,0,-39078,2981556] 2 [105:114:1] 80586i2 [1,-1,0,-625158,190409940] 2 [457:-219:1]
80586j (1 curve)	1	2+ 3- 11- 37+	2+ 3- -4  1 11-  3  3  5
Curve Equation t Generators 80586j1 [1,-1,0,1611,-1648971] 1 [129:768:1]
80586k (2 curves)	0	2+ 3- 11- 37-	2+ 3-  0  2 11-  2  2 -4
Curve Equation t 80586k1 [1,-1,0,-60462,-8793900] 2 80586k2 [1,-1,0,-1105902,-447251436] 2
80586l (2 curves)	0	2+ 3- 11- 37-	2+ 3-  0  2 11- -4  2  8
Curve Equation t 80586l1 [1,-1,0,-40233672,94613889024] 2 80586l2 [1,-1,0,19399968,351050467752] 2
80586m (2 curves)	2	2+ 3- 11- 37-	2+ 3-  0 -2 11- -2 -6  0
Curve Equation t Generators 80586m1 [1,-1,0,4878,396292] 2 [-36:434:1]&[-19:554:1] 80586m2 [1,-1,0,-60462,5192248] 2 [-228:2776:1]&[-118:3326:1]
80586n (2 curves)	0	2+ 3- 11- 37-	2+ 3-  0  4 11- -2 -6  7
Curve Equation t 80586n1 [1,-1,0,-398052,96795540] 1 80586n2 [1,-1,0,260793,373115133] 1
80586o (2 curves)	0	2+ 3- 11- 37-	2+ 3-  2 -2 11-  6 -2 -6
Curve Equation t 80586o1 [1,-1,0,-518931,-142379231] 2 80586o2 [1,-1,0,-116001,-358107953] 2
80586p (4 curves)	0	2+ 3- 11- 37-	2+ 3-  2  4 11- -6 -2  0
Curve Equation t 80586p1 [1,-1,0,-24814521,41038003309] 2 80586p2 [1,-1,0,-381658041,2869879323757] 4 80586p3 [1,-1,0,-366324921,3111023301997] 2 80586p4 [1,-1,0,-6106487481,183670297731949] 2
80586q (4 curves)	2	2+ 3- 11- 37-	2+ 3- -2  0 11- -6  6 -8
Curve Equation t Generators 80586q1 [1,-1,0,16857,-238595] 2 [17:221:1]&[838:12649:8] 80586q2 [1,-1,0,-70263,-1893875] 4 [-129:2303:1]&[2374:13393:8] 80586q3 [1,-1,0,-658323,204279961] 2 [-415:20354:1]&[278:6395:1] 80586q4 [1,-1,0,-876123,-315051071] 2 [-547:818:1]&[-525:323:1]
80586r (2 curves)	0	2+ 3- 11- 37-	2+ 3-  3 -2 11- -2  3 -2
Curve Equation t 80586r1 [1,-1,0,5967,1069173] 1 80586r2 [1,-1,0,-53928,-29585088] 1
80586s (1 curve)	0	2+ 3- 11- 37-	2+ 3- -3  4 11-  4  3  0
Curve Equation t 80586s1 [1,-1,0,-1629711,-5377870877] 1
80586t (1 curve)	0	2+ 3- 11- 37-	2+ 3-  4 -3 11- -3  3  7
Curve Equation t 80586t1 [1,-1,0,-198543780,1076851908688] 1
80586u (2 curves)	1	2- 3+ 11- 37+	2- 3+  2  0 11-  2 -2 -2
Curve Equation t Generators 80586u1 [1,-1,1,2881,5698663] 2 [19:2390:1] 80586u2 [1,-1,1,-461759,118513255] 2 [245:4354:1]
80586v (1 curve)	0	2- 3+ 11- 37-	2- 3+  2  3 11-  3 -3 -5
Curve Equation t 80586v1 [1,-1,1,-27974,1834165] 1
80586w (1 curve)	1	2- 3- 11+ 37+	2- 3-  1  4 11+  4 -5 -2
Curve Equation t Generators 80586w1 [1,-1,1,-104567,37113167] 1 [91:-5370:1]
80586x (1 curve)	1	2- 3- 11+ 37+	2- 3- -1  2 11+ -6 -1  8
Curve Equation t Generators 80586x1 [1,-1,1,-571748,188336063] 1 [1543:53799:1]
80586y (2 curves)	1	2- 3- 11+ 37+	2- 3-  2  2 11+  0  2  2
Curve Equation t Generators 80586y1 [1,-1,1,-6359,19055] 2 [-15:340:1] 80586y2 [1,-1,1,25321,133103] 2 [69:1450:1]
80586z (1 curve)	1	2- 3- 11+ 37+	2- 3- -3  0 11+  0  3 -6
Curve Equation t Generators 80586z1 [1,-1,1,-77144,-8227821] 1 [399:4739:1]
80586ba (2 curves)	1	2- 3- 11+ 37+	2- 3-  4 -2 11+ -2 -2 -8
Curve Equation t Generators 80586ba1 [1,-1,1,-3488,-84301] 2 [702:3875:8] 80586ba2 [1,-1,1,-56948,-5216461] 2 [657990:15222523:1000]
80586bb (2 curves)	0	2- 3- 11+ 37-	2- 3-  0  4 11+  2  2  6
Curve Equation t 80586bb1 [1,-1,1,-94865,9492189] 2 80586bb2 [1,-1,1,-1450175,672509841] 2
80586bc (2 curves)	0	2- 3- 11+ 37-	2- 3- -2  4 11+ -4  2 -8
Curve Equation t 80586bc1 [1,-1,1,-4728461,-3954265675] 2 80586bc2 [1,-1,1,-75644141,-253208697739] 2
80586bd (1 curve)	0	2- 3- 11- 37+	2- 3-  0 -3 11- -1 -3 -3
Curve Equation t 80586bd1 [1,-1,1,18490,6180243] 1
80586be (1 curve)	0	2- 3- 11- 37+	2- 3-  3  0 11-  4  5 -8
Curve Equation t 80586be1 [1,-1,1,41359,-1471071] 1
80586bf (2 curves)	1	2- 3- 11- 37-	2- 3-  0  1 11-  1 -3  7
Curve Equation t Generators 80586bf1 [1,-1,1,2155,-150235] 1 [105:1054:1] 80586bf2 [1,-1,1,-161195,-24887959] 1 [16086:697481:8]
80586bg (4 curves)	1	2- 3- 11- 37-	2- 3-  0  4 11-  4 -6 -2
Curve Equation t Generators 80586bg1 [1,-1,1,-1674905,306464249] 2 [-987:32074:1] 80586bg2 [1,-1,1,-14568665,-21184854919] 2 [-2171:15498:1] 80586bg3 [1,-1,1,-73548905,-242753004007] 2 [-339848139:65135432:68921] 80586bg4 [1,-1,1,-1176771245,-15537386236831] 2 [-1672179911685119:836396180461414:84431188603]
80586bh (2 curves)	1	2- 3- 11- 37-	2- 3-  0 -4 11-  2  6 -7
Curve Equation t Generators 80586bh1 [1,-1,1,-3290,-71827] 1 [12645:92273:125] 80586bh2 [1,-1,1,2155,-280915] 3 [201:2770:1]
80586bi (2 curves)	1	2- 3- 11- 37-	2- 3-  0 -4 11- -4  2  2
Curve Equation t Generators 80586bi1 [1,-1,1,-65974910,96808403981] 2 [-8423:238467:1] 80586bi2 [1,-1,1,-891175550,10234893386765] 2 [17625:43459:1]
80586bj (1 curve)	1	2- 3- 11- 37-	2- 3-  1  4 11- -4 -7  4
Curve Equation t Generators 80586bj1 [1,-1,1,-30152,2032363] 1 [113:185:1]

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