Cremona's table of elliptic curves

16800 = 2⁵ · 3 · 5² · 7

Class	r	Atkin-Lehner	Eigenvalues
16800a (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  0 -2 -2 -4
Curve Equation t Generators 16800a1 [0,-1,0,-558,-3888] 4 [-9:18:1] 16800a2 [0,-1,0,-8433,-295263] 2 [347:6200:1] 16800a3 [0,-1,0,-2808,54612] 2 [-12:294:1] 16800a4 [0,-1,0,1192,-24888] 2 [341:6318:1]
16800b (2 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  2  2 -4  4
Curve Equation t Generators 16800b1 [0,-1,0,42,-588] 2 [8:14:1] 16800b2 [0,-1,0,-833,-8463] 2 [-19:12:1]
16800c (1 curve)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+ -2  3 -1 -4
Curve Equation t Generators 16800c1 [0,-1,0,44792,-10778588] 1 [1412112:36967774:2197]
16800d (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+  4 -6  2 -4
Curve Equation t Generators 16800d1 [0,-1,0,-658,4312] 4 [-18:100:1] 16800d2 [0,-1,0,-4408,-108188] 2 [153:1666:1] 16800d3 [0,-1,0,-9408,354312] 2 [157:1650:1] 16800d4 [0,-1,0,1967,27937] 2 [3:184:1]
16800e (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+ -4  2  2  4
Curve Equation t Generators 16800e1 [0,-1,0,-506658,-138263688] 4 [93588468:1213772364:103823] 16800e2 [0,-1,0,-8100408,-8871076188] 2 [14259283092637:-1996095200124074:712121957] 16800e3 [0,-1,0,-725408,-7013688] 2 [9429233837223:-1330457607388950:472729139] 16800e4 [0,-1,0,-294033,-255420063] 2 [13141016913067846:-1854967643266015625:658957244408]
16800f (4 curves)	1	2+ 3+ 5+ 7+	2+ 3+ 5+ 7+ -4  2  2 -8
Curve Equation t Generators 16800f1 [0,-1,0,-131258,18343512] 4 [86:2772:1] 16800f2 [0,-1,0,-147008,13681512] 2 [61:2222:1] 16800f3 [0,-1,0,-2100008,1172031012] 4 [6938:12199:8] 16800f4 [0,-1,0,-115633,22859137] 2 [-168:6125:1]
16800g (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0 -2  2  4
Curve Equation t 16800g1 [0,-1,0,-22258,-1230488] 4 16800g2 [0,-1,0,-353008,-80610488] 2 16800g3 [0,-1,0,-56008,3427012] 4 16800g4 [0,-1,0,8367,-4384863] 2
16800h (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  0 -2  6 -4
Curve Equation t 16800h1 [0,-1,0,-4158,-68688] 4 16800h2 [0,-1,0,-60408,-5693688] 2 16800h3 [0,-1,0,-26033,1571937] 2 16800h4 [0,-1,0,11592,-478188] 2
16800i (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  4  6 -6  4
Curve Equation t 16800i1 [0,-1,0,-159468758,-775053481488] 4 16800i2 [0,-1,0,-2551500008,-49605979418988] 2 16800i3 [0,-1,0,-160015633,-769469340863] 2 16800i4 [0,-1,0,-158922008,-780632518488] 2
16800j (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7-  4 -6  6  4
Curve Equation t 16800j1 [0,-1,0,-1758,28512] 4 16800j2 [0,-1,0,-3633,-40863] 2 16800j3 [0,-1,0,-28008,1813512] 2 16800j4 [0,-1,0,-8,81012] 2
16800k (4 curves)	0	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -4  6  2  4
Curve Equation t 16800k1 [0,-1,0,-358,-2288] 4 16800k2 [0,-1,0,-5608,-159788] 2 16800k3 [0,-1,0,-1233,14337] 2 16800k4 [0,-1,0,392,-11288] 2
16800l (2 curves)	2	2+ 3+ 5+ 7-	2+ 3+ 5+ 7- -6 -4 -6 -6
Curve Equation t Generators 16800l1 [0,-1,0,-34258,2452012] 2 [-213:200:1]&[-18:1750:1] 16800l2 [0,-1,0,-33633,2545137] 2 [-143:2100:1]&[-63:2100:1]
16800m (1 curve)	0	2+ 3+ 5- 7+	2+ 3+ 5- 7+  2 -3  1  4
Curve Equation t 16800m1 [0,-1,0,1792,85512] 1
16800n (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  0 -2  6  4
Curve Equation t 16800n1 [0,1,0,-4158,68688] 4 16800n2 [0,1,0,-26033,-1571937] 2 16800n3 [0,1,0,-60408,5693688] 2 16800n4 [0,1,0,11592,478188] 2
16800o (1 curve)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -2 -3 -5  4
Curve Equation t 16800o1 [0,1,0,-288,-2052] 1
16800p (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  4  2  2  0
Curve Equation t 16800p1 [0,1,0,-1258,-8512] 4 16800p2 [0,1,0,-17008,-859012] 2 16800p3 [0,1,0,-10008,376488] 4 16800p4 [0,1,0,4367,-59137] 2
16800q (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  4  6  2 -4
Curve Equation t 16800q1 [0,1,0,-358,2288] 4 16800q2 [0,1,0,-1233,-14337] 2 16800q3 [0,1,0,-5608,159788] 2 16800q4 [0,1,0,392,11288] 2
16800r (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -4  6 -6 -4
Curve Equation t 16800r1 [0,1,0,-159468758,775053481488] 4 16800r2 [0,1,0,-160015633,769469340863] 2 16800r3 [0,1,0,-2551500008,49605979418988] 2 16800r4 [0,1,0,-158922008,780632518488] 2
16800s (4 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+ -4 -6  6 -4
Curve Equation t 16800s1 [0,1,0,-1758,-28512] 4 16800s2 [0,1,0,-28008,-1813512] 2 16800s3 [0,1,0,-3633,40863] 2 16800s4 [0,1,0,-8,-81012] 2
16800t (2 curves)	0	2+ 3- 5+ 7+	2+ 3- 5+ 7+  6 -4 -6  6
Curve Equation t 16800t1 [0,1,0,-34258,-2452012] 2 16800t2 [0,1,0,-33633,-2545137] 2
16800u (4 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  0 -2 -2  4
Curve Equation t Generators 16800u1 [0,1,0,-558,3888] 4 [-6:84:1] 16800u2 [0,1,0,-2808,-54612] 2 [63:150:1] 16800u3 [0,1,0,-8433,295263] 2 [69:216:1] 16800u4 [0,1,0,1192,24888] 2 [-2:150:1]
16800v (2 curves)	1	2+ 3- 5+ 7-	2+ 3- 5+ 7-  2  2  0  4
Curve Equation t Generators 16800v1 [0,1,0,5242,-210012] 2 [82:882:1] 16800v2 [0,1,0,-37633,-2225137] 2 [-121:756:1]
16800w (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  2 -2  0  6
Curve Equation t Generators 16800w1 [0,1,0,-22963458,-42362592912] 2 [135786:16891191:8] 16800w2 [0,1,0,-22962833,-42365013537] 2 [6658:316125:1]
16800x (1 curve)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  2  3  5 -4
Curve Equation t Generators 16800x1 [0,1,0,-7208,242088] 1 [58:-150:1]
16800y (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -2  2  0 -6
Curve Equation t Generators 16800y1 [0,1,0,-918538,338533328] 2 [533:810:1] 16800y2 [0,1,0,-918513,338552703] 2 [513:1620:1]
16800z (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  4  2 -6 -6
Curve Equation t Generators 16800z1 [0,1,0,42,-38412] 2 [42:198:1] 16800z2 [0,1,0,-16833,-831537] 2 [-81:84:1]
16800ba (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -4 -2  6  6
Curve Equation t Generators 16800ba1 [0,1,0,2,308] 2 [2:18:1] 16800ba2 [0,1,0,-673,6383] 2 [-1:84:1]
16800bb (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+  6 -6  0  2
Curve Equation t Generators 16800bb1 [0,1,0,-138,-672] 2 [106:9:8] 16800bb2 [0,1,0,-113,-897] 2 [33:180:1]
16800bc (2 curves)	1	2+ 3- 5- 7+	2+ 3- 5- 7+ -6  6  0 -2
Curve Equation t Generators 16800bc1 [0,1,0,-3458,77088] 2 [282:123:8] 16800bc2 [0,1,0,-2833,106463] 2 [17:252:1]
16800bd (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+  2  0  6 -6
Curve Equation t 16800bd1 [0,-1,0,-658,-6188] 2 16800bd2 [0,-1,0,-33,-18063] 2
16800be (2 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -2  2  0 -4
Curve Equation t 16800be1 [0,-1,0,5242,210012] 2 16800be2 [0,-1,0,-37633,2225137] 2
16800bf (4 curves)	0	2- 3+ 5+ 7+	2- 3+ 5+ 7+ -4  6 -6  0
Curve Equation t 16800bf1 [0,-1,0,-496158,134652312] 4 16800bf2 [0,-1,0,-557408,99372312] 2 16800bf3 [0,-1,0,-7938033,8610947937] 4 16800bf4 [0,-1,0,-435408,168793812] 2
16800bg (1 curve)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  2 -3 -5 -4
Curve Equation t Generators 16800bg1 [0,-1,0,-288,2052] 1 [8:14:1]
16800bh (2 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7-  2  4  2 -6
Curve Equation t Generators 16800bh1 [0,-1,0,-5258,123012] 2 [-53:500:1] 16800bh2 [0,-1,0,10367,701137] 2 [27:1000:1]
16800bi (4 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -4  2  2  0
Curve Equation t Generators 16800bi1 [0,-1,0,-1258,8512] 4 [-13:150:1] 16800bi2 [0,-1,0,-10008,-376488] 2 [954:2673:8] 16800bi3 [0,-1,0,-17008,859012] 2 [-48:1250:1] 16800bi4 [0,-1,0,4367,59137] 4 [1:252:1]
16800bj (4 curves)	1	2- 3+ 5+ 7-	2- 3+ 5+ 7- -4 -2  2  0
Curve Equation t Generators 16800bj1 [0,-1,0,-108158,-11105688] 4 [-132:924:1] 16800bj2 [0,-1,0,-1639408,-807355688] 2 [-159762:41041:216] 16800bj3 [0,-1,0,-530033,138659937] 4 [-753:10500:1] 16800bj4 [0,-1,0,222592,-66010188] 2 [4593:312774:1]
16800bk (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  2  2  0  6
Curve Equation t 16800bk1 [0,-1,0,-918538,-338533328] 2 16800bk2 [0,-1,0,-918513,-338552703] 2
16800bl (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -2 -2  0 -6
Curve Equation t 16800bl1 [0,-1,0,-22963458,42362592912] 2 16800bl2 [0,-1,0,-22962833,42365013537] 2
16800bm (1 curve)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -2  3  5  4
Curve Equation t 16800bm1 [0,-1,0,-7208,-242088] 1
16800bn (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  4 -2  6 -6
Curve Equation t 16800bn1 [0,-1,0,2,-308] 2 16800bn2 [0,-1,0,-673,-6383] 2
16800bo (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7- -4  2 -6  6
Curve Equation t 16800bo1 [0,-1,0,42,38412] 2 16800bo2 [0,-1,0,-16833,831537] 2
16800bp (2 curves)	0	2- 3+ 5- 7-	2- 3+ 5- 7-  6  6  0  2
Curve Equation t 16800bp1 [0,-1,0,-3458,-77088] 2 16800bp2 [0,-1,0,-2833,-106463] 2
16800bq (2 curves)	2	2- 3+ 5- 7-	2- 3+ 5- 7- -6 -6  0 -2
Curve Equation t Generators 16800bq1 [0,-1,0,-138,672] 2 [-13:10:1]&[2:20:1] 16800bq2 [0,-1,0,-113,897] 2 [-8:35:1]&[-7:36:1]
16800br (4 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  0 -2  2 -4
Curve Equation t Generators 16800br1 [0,1,0,-22258,1230488] 4 [-52:1500:1] 16800br2 [0,1,0,-56008,-3427012] 2 [-97:1050:1] 16800br3 [0,1,0,-353008,80610488] 2 [218:3750:1] 16800br4 [0,1,0,8367,4384863] 4 [-102:1575:1]
16800bs (2 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+ -2  4  2  6
Curve Equation t Generators 16800bs1 [0,1,0,-5258,-123012] 2 [-47:150:1] 16800bs2 [0,1,0,10367,-701137] 2 [98:1125:1]
16800bt (4 curves)	1	2- 3- 5+ 7+	2- 3- 5+ 7+  4 -2  2  0
Curve Equation t Generators 16800bt1 [0,1,0,-108158,11105688] 4 [-323:3528:1] 16800bt2 [0,1,0,-530033,-138659937] 2 [-497:1500:1] 16800bt3 [0,1,0,-1639408,807355688] 4 [-1282:28350:1] 16800bt4 [0,1,0,222592,66010188] 2 [-173:4728:1]
16800bu (1 curve)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  2  3 -1  4
Curve Equation t 16800bu1 [0,1,0,44792,10778588] 1
16800bv (2 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -2  0  6  6
Curve Equation t 16800bv1 [0,1,0,-658,6188] 2 16800bv2 [0,1,0,-33,18063] 2
16800bw (2 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -2  2 -4 -4
Curve Equation t 16800bw1 [0,1,0,42,588] 2 16800bw2 [0,1,0,-833,8463] 2
16800bx (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4  2  2 -4
Curve Equation t 16800bx1 [0,1,0,-506658,138263688] 4 16800bx2 [0,1,0,-725408,7013688] 2 16800bx3 [0,1,0,-8100408,8871076188] 2 16800bx4 [0,1,0,-294033,255420063] 2
16800by (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4  2  2  8
Curve Equation t 16800by1 [0,1,0,-131258,-18343512] 4 16800by2 [0,1,0,-2100008,-1172031012] 2 16800by3 [0,1,0,-147008,-13681512] 2 16800by4 [0,1,0,-115633,-22859137] 4
16800bz (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7-  4  6 -6  0
Curve Equation t 16800bz1 [0,1,0,-496158,-134652312] 4 16800bz2 [0,1,0,-7938033,-8610947937] 2 16800bz3 [0,1,0,-557408,-99372312] 4 16800bz4 [0,1,0,-435408,-168793812] 2
16800ca (4 curves)	0	2- 3- 5+ 7-	2- 3- 5+ 7- -4 -6  2  4
Curve Equation t 16800ca1 [0,1,0,-658,-4312] 4 16800ca2 [0,1,0,-9408,-354312] 2 16800ca3 [0,1,0,-4408,108188] 2 16800ca4 [0,1,0,1967,-27937] 2
16800cb (1 curve)	1	2- 3- 5- 7-	2- 3- 5- 7- -2 -3  1 -4
Curve Equation t Generators 16800cb1 [0,1,0,1792,-85512] 1 [178:-2430:1]

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

Part of Computational Number Theory
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