Cremona's table of elliptic curves

27342 = 2 · 3² · 7² · 31

Class	r	Atkin-Lehner	Eigenvalues
27342a (2 curves)	0	2+ 3+ 7- 31+	2+ 3+ -3 7-  3 -5 -3  7
Curve Equation t 27342a1 [1,-1,0,-2361,-94067] 1 27342a2 [1,-1,0,20424,2040128] 1
27342b (1 curve)	1	2+ 3+ 7- 31-	2+ 3+  1 7- -3  1  3 -1
Curve Equation t Generators 27342b1 [1,-1,0,-9,-673] 1 [37:202:1]
27342c (1 curve)	1	2+ 3+ 7- 31-	2+ 3+  1 7-  5  1 -5 -1
Curve Equation t Generators 27342c1 [1,-1,0,-18849819,32196867877] 1 [805268:85148573:64]
27342d (1 curve)	0	2+ 3- 7+ 31+	2+ 3-  0 7+ -4  1  4  0
Curve Equation t 27342d1 [1,-1,0,138,-820] 1
27342e (1 curve)	0	2+ 3- 7+ 31+	2+ 3- -4 7+ -4 -1 -4  4
Curve Equation t 27342e1 [1,-1,0,-6624,-207306] 1
27342f (2 curves)	1	2+ 3- 7- 31+	2+ 3-  1 7-  3  1  3  5
Curve Equation t Generators 27342f1 [1,-1,0,6606,70132] 1 [-26:1777:8] 27342f2 [1,-1,0,-615204,-185665838] 1 [1177844950:113331455257:125000]
27342g (1 curve)	1	2+ 3- 7- 31+	2+ 3-  1 7-  5  5 -3  1
Curve Equation t Generators 27342g1 [1,-1,0,-9,85077] 1 [-33:237:1]
27342h (4 curves)	1	2+ 3- 7- 31+	2+ 3-  2 7- -4 -2 -2  0
Curve Equation t Generators 27342h1 [1,-1,0,-18531,-963131] 2 [-75:62:1] 27342h2 [1,-1,0,-27351,54697] 4 [-4:407:1] 27342h3 [1,-1,0,109359,355459] 2 [4553:305726:1] 27342h4 [1,-1,0,-305181,64789087] 2 [339:283:1]
27342i (4 curves)	1	2+ 3- 7- 31+	2+ 3- -2 7-  0 -2  6 -4
Curve Equation t Generators 27342i1 [1,-1,0,-881568,-318361856] 2 [-4338:2855:8] 27342i2 [1,-1,0,-916848,-291471440] 4 [-568:7052:1] 27342i3 [1,-1,0,1543932,-1588302500] 2 [127700:-6279835:64] 27342i4 [1,-1,0,-3942108,2725922884] 2 [-1552:72218:1]
27342j (6 curves)	1	2+ 3- 7- 31+	2+ 3- -2 7- -4  2 -6  4
Curve Equation t Generators 27342j1 [1,-1,0,-45873,-449068131] 2 [1353:43644:1] 27342j2 [1,-1,0,-9077553,-10382109795] 4 [-3572166:-17490621:2197] 27342j3 [1,-1,0,-17968113,13297007709] 2 [-2406:207591:1] 27342j4 [1,-1,0,-144693873,-669884273955] 4 [-4588622394135:2045992431900:660776311] 27342j5 [1,-1,0,-144147033,-675199230651] 2 [11885095278597994536681:-2288207648899665122638068:291211442320002191] 27342j6 [1,-1,0,-2315101833,-42874335219339] 2 [-9629153087987779366794735:4814580729802564222656396:346631143776909808375]
27342k (3 curves)	1	2+ 3- 7- 31+	2+ 3-  3 7-  0  4 -6 -2
Curve Equation t Generators 27342k1 [1,-1,0,-1773,151717] 1 [-33:433:1] 27342k2 [1,-1,0,15867,-3958403] 1 [68955:1606949:125] 27342k3 [1,-1,0,-1487943,-698581913] 1 [389476475747385:-10227097042062697:223096324625]
27342l (2 curves)	1	2+ 3- 7- 31+	2+ 3- -4 7-  6  2 -2  8
Curve Equation t Generators 27342l1 [1,-1,0,-83799,3080349] 2 [37:153:1] 27342l2 [1,-1,0,-1071639,426863709] 2 [822:-10455:1]
27342m (1 curve)	0	2+ 3- 7- 31-	2+ 3-  0 7- -4 -1 -4  0
Curve Equation t 27342m1 [1,-1,0,6753,267749] 1
27342n (1 curve)	0	2+ 3- 7- 31-	2+ 3-  1 7- -1 -5 -5  5
Curve Equation t 27342n1 [1,-1,0,-101439,-12410609] 1
27342o (4 curves)	0	2+ 3- 7- 31-	2+ 3-  2 7-  0  2  2 -8
Curve Equation t 27342o1 [1,-1,0,-1603926,760901364] 2 27342o2 [1,-1,0,-3861846,-1855124748] 4 27342o3 [1,-1,0,11449674,-12925353708] 2 27342o4 [1,-1,0,-55300086,-158237661996] 2
27342p (2 curves)	0	2+ 3- 7- 31-	2+ 3-  2 7-  6 -4  2  4
Curve Equation t 27342p1 [1,-1,0,-14121,693657] 2 27342p2 [1,-1,0,-230211,42571899] 2
27342q (4 curves)	2	2+ 3- 7- 31-	2+ 3- -2 7-  0 -2 -6 -4
Curve Equation t Generators 27342q1 [1,-1,0,-303,10205] 2 [-82:923:8]&[2:-99:1] 27342q2 [1,-1,0,-9123,336545] 4 [65:-155:1]&[-38:811:1] 27342q3 [1,-1,0,-13533,-18901] 2 [-95:682:1]&[-61:790:1] 27342q4 [1,-1,0,-145833,21471911] 2 [223:-53:1]&[277:1369:1]
27342r (2 curves)	0	2+ 3- 7- 31-	2+ 3- -2 7-  2  4 -2  8
Curve Equation t 27342r1 [1,-1,0,9252,435280] 2 27342r2 [1,-1,0,-61308,4428976] 2
27342s (1 curve)	0	2+ 3- 7- 31-	2+ 3- -3 7-  3  3 -5  1
Curve Equation t 27342s1 [1,-1,0,-552141,174322021] 1
27342t (1 curve)	0	2+ 3- 7- 31-	2+ 3- -3 7- -4 -4  2 -6
Curve Equation t 27342t1 [1,-1,0,-1042386,-409368772] 1
27342u (1 curve)	0	2+ 3- 7- 31-	2+ 3-  4 7- -4  1  4 -4
Curve Equation t 27342u1 [1,-1,0,-135,643] 1
27342v (2 curves)	0	2+ 3- 7- 31-	2+ 3-  4 7-  6 -2  2 -8
Curve Equation t 27342v1 [1,-1,0,-1710,-8492] 2 27342v2 [1,-1,0,-21870,-1238252] 2
27342w (2 curves)	1	2- 3+ 7- 31+	2- 3+  3 7- -3 -5  3  7
Curve Equation t Generators 27342w1 [1,-1,1,2269,-76317] 1 [107:1122:1] 27342w2 [1,-1,1,-21251,2561059] 1 [121:1262:1]
27342x (1 curve)	0	2- 3+ 7- 31-	2- 3+ -1 7-  3  1 -3 -1
Curve Equation t 27342x1 [1,-1,1,-83,18253] 1
27342y (1 curve)	0	2- 3+ 7- 31-	2- 3+ -1 7- -5  1  5 -1
Curve Equation t 27342y1 [1,-1,1,-169648373,-869145784307] 1
27342z (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7-  0 -4  4  8
Curve Equation t 27342z1 [1,-1,1,45340,-1727225] 2 27342z2 [1,-1,1,-201620,-14371577] 2
27342ba (2 curves)	0	2- 3- 7- 31+	2- 3-  0 7-  6  2  6 -6
Curve Equation t 27342ba1 [1,-1,1,-4640,30111] 2 27342ba2 [1,-1,1,-44330,-3557865] 2
27342bb (4 curves)	0	2- 3- 7- 31+	2- 3-  0 7- -6 -2  6  4
Curve Equation t 27342bb1 [1,-1,1,-81815,7537695] 2 27342bb2 [1,-1,1,156325,43068183] 2 27342bb3 [1,-1,1,-1887710,-997040019] 2 27342bb4 [1,-1,1,-1464350,-1456639635] 2
27342bc (1 curve)	0	2- 3- 7- 31+	2- 3- -1 7- -3 -3  1 -7
Curve Equation t 27342bc1 [1,-1,1,-36833,-3086485] 1
27342bd (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0  2 -2  2
Curve Equation t 27342bd1 [1,-1,1,-13649,-604159] 2 27342bd2 [1,-1,1,-217769,-39060367] 2
27342be (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0  6 -2  2
Curve Equation t 27342be1 [1,-1,1,-83579,-8166805] 2 27342be2 [1,-1,1,128101,-42966997] 2
27342bf (2 curves)	0	2- 3- 7- 31+	2- 3-  2 7-  0 -6  6 -2
Curve Equation t 27342bf1 [1,-1,1,-419,-2145] 2 27342bf2 [1,-1,1,-6089,-181317] 2
27342bg (2 curves)	0	2- 3- 7- 31+	2- 3- -2 7-  2 -4  0  4
Curve Equation t 27342bg1 [1,-1,1,12603109,1476175691] 2 27342bg2 [1,-1,1,-50618651,11869833035] 2
27342bh (2 curves)	0	2- 3- 7- 31+	2- 3- -2 7-  4  2  6  2
Curve Equation t 27342bh1 [1,-1,1,-2212286,1198798157] 2 27342bh2 [1,-1,1,-6657566,-5127724339] 2
27342bi (2 curves)	0	2- 3- 7- 31+	2- 3-  3 7-  3  1  3  1
Curve Equation t 27342bi1 [1,-1,1,32404,49965423] 1 27342bi2 [1,-1,1,-291731,-1351594317] 1
27342bj (1 curve)	0	2- 3- 7- 31+	2- 3-  3 7- -6  2 -2  2
Curve Equation t 27342bj1 [1,-1,1,-146,739] 1
27342bk (2 curves)	0	2- 3- 7- 31+	2- 3-  4 7-  2  2  6 -2
Curve Equation t 27342bk1 [1,-1,1,-4797428,4045595159] 2 27342bk2 [1,-1,1,-4956188,3763637399] 2
27342bl (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  0  4 -4 -8
Curve Equation t Generators 27342bl1 [1,-1,1,925,4771] 2 [-1:62:1] 27342bl2 [1,-1,1,-4115,43075] 2 [-59:308:1]
27342bm (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7-  2  2  2  6
Curve Equation t Generators 27342bm1 [1,-1,1,-3170,-43487] 2 [79:401:1] 27342bm2 [1,-1,1,-20810,1127809] 2 [107:289:1]
27342bn (2 curves)	1	2- 3- 7- 31-	2- 3-  0 7- -2 -2  2  2
Curve Equation t Generators 27342bn1 [1,-1,1,-2807195,1600731339] 2 [-117:43962:1] 27342bn2 [1,-1,1,-43449755,110246422731] 2 [4307:-56838:1]
27342bo (2 curves)	1	2- 3- 7- 31-	2- 3-  2 7-  4 -2 -6 -2
Curve Equation t Generators 27342bo1 [1,-1,1,-45149,-3482139] 2 [-117:492:1] 27342bo2 [1,-1,1,-135869,14988453] 2 [531:9344:1]
27342bp (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  0  2 -6 -2
Curve Equation t Generators 27342bp1 [1,-1,1,-4143866,-2925187275] 2 [-123566051572:-1503756093201:131096512] 27342bp2 [1,-1,1,5500804,-14529654219] 2 [163084621190942953204:-24468279762824004056943:7365249423278144]
27342bq (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  0 -2  2 -2
Curve Equation t Generators 27342bq1 [1,-1,1,-668786,208564017] 2 [429:471:1] 27342bq2 [1,-1,1,-10670666,13419047121] 2 [1887:-901:1]
27342br (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  0  6 -6  2
Curve Equation t Generators 27342br1 [1,-1,1,-20516,776675] 2 [-586:11265:8] 27342br2 [1,-1,1,-298346,62788331] 2 [4598:69665:8]
27342bs (2 curves)	1	2- 3- 7- 31-	2- 3- -2 7-  6 -4  0  4
Curve Equation t Generators 27342bs1 [1,-1,1,-13901,1048821] 2 [51:-712:1] 27342bs2 [1,-1,1,-260861,51329877] 2 [345:-1692:1]
27342bt (1 curve)	1	2- 3- 7- 31-	2- 3-  3 7- -5  7 -1 -7
Curve Equation t Generators 27342bt1 [1,-1,1,-7286,-242427] 1 [107:387:1]
27342bu (1 curve)	1	2- 3- 7- 31-	2- 3- -3 7- -6 -2  2 -2
Curve Equation t Generators 27342bu1 [1,-1,1,-7139,-239291] 1 [54185948:352574101:438976]

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