Cremona's table of elliptic curves

42075 = 3² · 5² · 11 · 17

Class	r	Atkin-Lehner	Eigenvalues
42075a (2 curves)	1	3+ 5+ 11+ 17+	1 3+ 5+  2 11+  2 17+  2
Curve Equation t Generators 42075a1 [1,-1,0,-18810942,31301759591] 2 [-901968443788463730:38077888085634879953:209298916728117] 42075a2 [1,-1,0,-300694317,2007022334966] 2 [3942538183978:-2014105806314:393832837]
42075b (1 curve)	1	3+ 5+ 11+ 17+	1 3+ 5+ -3 11+ -3 17+ -3
Curve Equation t Generators 42075b1 [1,-1,0,11433,-444034] 1 [118:1534:1]
42075c (2 curves)	1	3+ 5+ 11+ 17+	-1 3+ 5+  0 11+  4 17+  2
Curve Equation t Generators 42075c1 [1,-1,1,-1463105,-296757728] 2 [-1750450:42715951:2197] 42075c2 [1,-1,1,-12009980,15818867272] 2 [1718:15085:1]
42075d (2 curves)	1	3+ 5+ 11+ 17+	-1 3+ 5+  0 11+ -4 17+  2
Curve Equation t Generators 42075d1 [1,-1,1,-3755,68122] 2 [74:400:1] 42075d2 [1,-1,1,-20630,-1079378] 2 [-76:250:1]
42075e (1 curve)	1	3+ 5+ 11+ 17+	-1 3+ 5+  3 11+  5 17+ -7
Curve Equation t Generators 42075e1 [1,-1,1,-1058359880,-13252680654128] 1 [35252272789100219561820341299882346911888150669750:-20183383018677280824578440393602042793766187561872191:106645684430079289883498819521190203861328125]
42075f (2 curves)	0	3+ 5+ 11+ 17-	-1 3+ 5+  2 11+  2 17-  8
Curve Equation t 42075f1 [1,-1,1,-1655,-16778] 2 42075f2 [1,-1,1,4720,-118778] 2
42075g (1 curve)	2	3+ 5+ 11+ 17-	-1 3+ 5+ -3 11+  1 17- -1
Curve Equation t Generators 42075g1 [1,-1,1,-35480,2618272] 1 [529:11210:1]&[-46:2060:1]
42075h (2 curves)	0	3+ 5+ 11- 17+	1 3+ 5+  2 11-  2 17+  8
Curve Equation t 42075h1 [1,-1,0,-14892,467891] 2 42075h2 [1,-1,0,42483,3164516] 2
42075i (1 curve)	0	3+ 5+ 11- 17+	1 3+ 5+ -3 11-  1 17+ -1
Curve Equation t 42075i1 [1,-1,0,-3942,-95659] 1
42075j (2 curves)	1	3+ 5+ 11- 17-	1 3+ 5+  0 11-  4 17-  2
Curve Equation t Generators 42075j1 [1,-1,0,-162567,11045216] 2 [7982:228059:8] 42075j2 [1,-1,0,-1334442,-585439159] 2 [2864:136693:1]
42075k (2 curves)	1	3+ 5+ 11- 17-	1 3+ 5+  0 11- -4 17-  2
Curve Equation t Generators 42075k1 [1,-1,0,-417,-2384] 2 [-12:34:1] 42075k2 [1,-1,0,-2292,40741] 2 [-36:293:1]
42075l (1 curve)	1	3+ 5+ 11- 17-	1 3+ 5+  3 11-  5 17- -7
Curve Equation t Generators 42075l1 [1,-1,0,-117595542,490879222741] 1 [-2196:860473:1]
42075m (2 curves)	1	3+ 5+ 11- 17-	-1 3+ 5+  2 11-  2 17-  2
Curve Equation t Generators 42075m1 [1,-1,1,-2090105,-1158627728] 2 [-830:2378:1] 42075m2 [1,-1,1,-33410480,-74323023728] 2 [-1144465:570004:343]
42075n (1 curve)	1	3+ 5+ 11- 17-	-1 3+ 5+ -3 11- -3 17- -3
Curve Equation t Generators 42075n1 [1,-1,1,1270,16022] 1 [34:295:1]
42075o (2 curves)	0	3+ 5- 11+ 17+	-1 3+ 5-  0 11+  4 17+ -8
Curve Equation t 42075o1 [1,-1,1,-35180,-2763178] 2 42075o2 [1,-1,1,-577055,-168576928] 2
42075p (2 curves)	1	3+ 5- 11+ 17-	1 3+ 5-  0 11+ -4 17- -8
Curve Equation t Generators 42075p1 [1,-1,0,-1407,-21824] 2 [454:2017:8] 42075p2 [1,-1,0,-23082,-1343999] 2 [3174:56009:8]
42075q (2 curves)	1	3+ 5- 11- 17+	-1 3+ 5-  0 11- -4 17+ -8
Curve Equation t Generators 42075q1 [1,-1,1,-12665,601912] 2 [4:740:1] 42075q2 [1,-1,1,-207740,36495712] 2 [260:-37:1]
42075r (2 curves)	0	3+ 5- 11- 17-	1 3+ 5-  0 11-  4 17- -8
Curve Equation t 42075r1 [1,-1,0,-316617,74922416] 2 42075r2 [1,-1,0,-5193492,4556770541] 2
42075s (1 curve)	0	3- 5+ 11+ 17+	0 3- 5+ -1 11+  6 17+ -6
Curve Equation t 42075s1 [0,0,1,-60600,-5798219] 1
42075t (2 curves)	0	3- 5+ 11+ 17+	0 3- 5+ -2 11+ -2 17+  2
Curve Equation t 42075t1 [0,0,1,2400,-89969] 1 42075t2 [0,0,1,-22350,2941906] 1
42075u (1 curve)	0	3- 5+ 11+ 17+	0 3- 5+  3 11+ -2 17+  2
Curve Equation t 42075u1 [0,0,1,-839100,295848531] 1
42075v (4 curves)	0	3- 5+ 11+ 17+	1 3- 5+  0 11+ -2 17+  4
Curve Equation t 42075v1 [1,-1,0,20808,1056091] 2 42075v2 [1,-1,0,-115317,9904216] 4 42075v3 [1,-1,0,-746442,-240652409] 2 42075v4 [1,-1,0,-1662192,825107341] 2
42075w (4 curves)	0	3- 5+ 11+ 17+	1 3- 5+  0 11+ -2 17+ -8
Curve Equation t 42075w1 [1,-1,0,-3088917,1317456616] 2 42075w2 [1,-1,0,-20667042,-35192309009] 4 42075w3 [1,-1,0,5629833,-118632293384] 2 42075w4 [1,-1,0,-328213917,-2288588262134] 2
42075x (4 curves)	0	3- 5+ 11+ 17+	1 3- 5+ -4 11+  2 17+  4
Curve Equation t 42075x1 [1,-1,0,-25542,-801009] 2 42075x2 [1,-1,0,-350667,-79806384] 4 42075x3 [1,-1,0,-293292,-106830009] 2 42075x4 [1,-1,0,-5610042,-5113028259] 2
42075y (1 curve)	0	3- 5+ 11+ 17+	-2 3- 5+  3 11+  4 17+ -2
Curve Equation t 42075y1 [0,0,1,-1875,-37094] 1
42075z (1 curve)	0	3- 5+ 11+ 17+	-2 3- 5+  5 11+  2 17+  4
Curve Equation t 42075z1 [0,0,1,105,-684] 1
42075ba (1 curve)	1	3- 5+ 11+ 17-	0 3- 5+ -3 11+  0 17-  0
Curve Equation t Generators 42075ba1 [0,0,1,-300,11281] 1 [-5:112:1]
42075bb (1 curve)	1	3- 5+ 11+ 17-	0 3- 5+ -3 11+ -3 17- -3
Curve Equation t Generators 42075bb1 [0,0,1,-54476602500,-4894011040799219] 1 [34702555:4642266616:125]
42075bc (1 curve)	1	3- 5+ 11+ 17-	0 3- 5+  4 11+  4 17-  4
Curve Equation t Generators 42075bc1 [0,0,1,-210,1201] 1 [1:31:1]
42075bd (1 curve)	1	3- 5+ 11+ 17-	0 3- 5+ -4 11+  4 17-  4
Curve Equation t Generators 42075bd1 [0,0,1,48772500,17089569531] 1 [4229860815308506577308117:-102495402604365999639900516688:7203929595283637]
42075be (4 curves)	1	3- 5+ 11+ 17-	-1 3- 5+  0 11+  2 17-  8
Curve Equation t Generators 42075be1 [1,-1,1,-2705,-53328] 2 [-30:26:1] 42075be2 [1,-1,1,-3830,-3828] 4 [-52:255:1] 42075be3 [1,-1,1,15295,-42078] 2 [23:555:1] 42075be4 [1,-1,1,-40955,3188922] 2 [-196:2010:1]
42075bf (2 curves)	1	3- 5+ 11- 17+	0 3- 5+ -5 11-  4 17+ -4
Curve Equation t Generators 42075bf1 [0,0,1,-2959950,-1960086344] 1 [10960:1132312:1] 42075bf2 [0,0,1,-2172450,-3025770719] 1 [2335:68062:1]
42075bg (1 curve)	1	3- 5+ 11- 17+	1 3- 5+ -3 11- -5 17+ -4
Curve Equation t Generators 42075bg1 [1,-1,0,408,-3979] 1 [20:99:1]
42075bh (1 curve)	1	3- 5+ 11- 17+	-2 3- 5+  0 11-  4 17+  2
Curve Equation t Generators 42075bh1 [0,0,1,-635625,195053906] 1 [456:166:1]
42075bi (2 curves)	0	3- 5+ 11- 17-	0 3- 5+  1 11- -2 17-  2
Curve Equation t 42075bi1 [0,0,1,-421050,-108202469] 1 42075bi2 [0,0,1,1988700,-381709094] 1
42075bj (1 curve)	0	3- 5+ 11- 17-	1 3- 5+  3 11-  1 17-  2
Curve Equation t 42075bj1 [1,-1,0,-252582,-49249279] 1
42075bk (1 curve)	0	3- 5+ 11- 17-	1 3- 5+  3 11- -4 17-  2
Curve Equation t 42075bk1 [1,-1,0,-39807,3066916] 1
42075bl (1 curve)	0	3- 5+ 11- 17-	1 3- 5+ -3 11-  5 17-  2
Curve Equation t 42075bl1 [1,-1,0,378,-1679] 1
42075bm (4 curves)	0	3- 5+ 11- 17-	-1 3- 5+  0 11- -6 17-  0
Curve Equation t 42075bm1 [1,-1,1,-56480,-3201478] 2 42075bm2 [1,-1,1,-381605,88483772] 4 42075bm3 [1,-1,1,96520,295033772] 2 42075bm4 [1,-1,1,-6061730,5745888272] 2
42075bn (1 curve)	0	3- 5+ 11- 17-	-1 3- 5+  3 11-  0 17-  6
Curve Equation t 42075bn1 [1,-1,1,-5,-88] 1
42075bo (1 curve)	0	3- 5+ 11- 17-	2 3- 5+  5 11- -4 17-  2
Curve Equation t 42075bo1 [0,0,1,1575,-4219] 1
42075bp (1 curve)	0	3- 5+ 11- 17-	-2 3- 5+  3 11- -2 17- -4
Curve Equation t 42075bp1 [0,0,1,-28125,-2046094] 1
42075bq (1 curve)	0	3- 5+ 11- 17-	-2 3- 5+  3 11-  5 17- -7
Curve Equation t 42075bq1 [0,0,1,-463125,-161427344] 1
42075br (1 curve)	0	3- 5+ 11- 17-	-2 3- 5+ -3 11- -4 17-  2
Curve Equation t 42075br1 [0,0,1,-4035,-98654] 1
42075bs (1 curve)	1	3- 5- 11+ 17+	0 3- 5-  3 11+  3 17+ -3
Curve Equation t Generators 42075bs1 [0,0,1,-2179064100,-39152088326394] 1 [628569173290990950655974145229496536762:-104916140530996929239972551623038499581330:9214313881873046253519069582188023]
42075bt (1 curve)	1	3- 5- 11+ 17+	0 3- 5-  4 11+ -4 17+  4
Curve Equation t Generators 42075bt1 [0,0,1,1950900,136716556] 1 [15458:843629:8]
42075bu (1 curve)	1	3- 5- 11+ 17+	0 3- 5- -4 11+ -4 17+  4
Curve Equation t Generators 42075bu1 [0,0,1,-5250,150156] 1 [50:-113:1]
42075bv (2 curves)	1	3- 5- 11+ 17+	1 3- 5-  4 11+  2 17+ -6
Curve Equation t Generators 42075bv1 [1,-1,0,3258,19791] 2 [-2030:6707:343] 42075bv2 [1,-1,0,-13617,171666] 2 [-122:138:1]
42075bw (1 curve)	1	3- 5- 11+ 17+	1 3- 5- -5 11+ -7 17+  3
Curve Equation t Generators 42075bw1 [1,-1,0,-55197,-4978314] 1 [858:23628:1]
42075bx (2 curves)	1	3- 5- 11+ 17+	-1 3- 5-  0 11+ -2 17+  4
Curve Equation t Generators 42075bx1 [1,-1,1,265,-3058] 2 [18:76:1] 42075bx2 [1,-1,1,-2210,-32758] 2 [-30:91:1]
42075by (2 curves)	0	3- 5- 11+ 17-	1 3- 5-  0 11+  2 17-  4
Curve Equation t 42075by1 [1,-1,0,6633,-375584] 2 42075by2 [1,-1,0,-55242,-4149959] 2
42075bz (2 curves)	2	3- 5- 11+ 17-	-1 3- 5- -4 11+ -2 17- -6
Curve Equation t Generators 42075bz1 [1,-1,1,130,132] 2 [0:11:1]&[22:165:8] 42075bz2 [1,-1,1,-545,1482] 2 [-22:60:1]&[-98:675:8]
42075ca (1 curve)	0	3- 5- 11+ 17-	-1 3- 5-  5 11+  7 17-  3
Curve Equation t 42075ca1 [1,-1,1,-1379930,-623669178] 1
42075cb (1 curve)	0	3- 5- 11+ 17-	2 3- 5- -5 11+ -2 17-  4
Curve Equation t 42075cb1 [0,0,1,2625,-85469] 1
42075cc (1 curve)	0	3- 5- 11- 17+	1 3- 5- -3 11-  0 17+  6
Curve Equation t 42075cc1 [1,-1,0,-117,-11084] 1
42075cd (1 curve)	2	3- 5- 11- 17+	-1 3- 5- -1 11- -5 17+ -5
Curve Equation t Generators 42075cd1 [1,-1,1,-500,5852] 1 [-26:40:1]&[18:40:1]
42075ce (1 curve)	0	3- 5- 11- 17+	-1 3- 5-  3 11- -5 17+  2
Curve Equation t 42075ce1 [1,-1,1,9445,-200428] 1
42075cf (1 curve)	0	3- 5- 11- 17+	-1 3- 5- -3 11- -1 17+  2
Curve Equation t 42075cf1 [1,-1,1,-6314555,-6162474428] 1
42075cg (1 curve)	0	3- 5- 11- 17+	-1 3- 5- -3 11-  4 17+  2
Curve Equation t 42075cg1 [1,-1,1,-995180,382369322] 1
42075ch (1 curve)	0	3- 5- 11- 17+	2 3- 5-  3 11-  4 17+  2
Curve Equation t 42075ch1 [0,0,1,-100875,-12331719] 1
42075ci (1 curve)	0	3- 5- 11- 17+	2 3- 5- -3 11-  2 17+ -4
Curve Equation t 42075ci1 [0,0,1,-1125,-16369] 1
42075cj (1 curve)	0	3- 5- 11- 17+	2 3- 5- -3 11- -5 17+ -7
Curve Equation t 42075cj1 [0,0,1,-18525,-1291419] 1
42075ck (1 curve)	1	3- 5- 11- 17-	1 3- 5-  1 11-  5 17- -5
Curve Equation t Generators 42075ck1 [1,-1,0,-12492,719041] 1 [144:1303:1]
42075cl (1 curve)	1	3- 5- 11- 17-	-1 3- 5-  3 11-  5 17- -4
Curve Equation t Generators 42075cl1 [1,-1,1,10195,-487178] 1 [44:190:1]
42075cm (1 curve)	1	3- 5- 11- 17-	2 3- 5-  0 11- -4 17-  2
Curve Equation t Generators 42075cm1 [0,0,1,-25425,1560431] 1 [690:761:8]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

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