Cremona's table of elliptic curves

17856 = 2⁶ · 3² · 31

Class	r	Atkin-Lehner	Eigenvalues
17856a (1 curve)	1	2+ 3+ 31+	2+ 3+  1  0  3  1 -3 -1
Curve Equation t Generators 17856a1 [0,0,0,-12,1008] 1 [-2:32:1]
17856b (1 curve)	1	2+ 3+ 31+	2+ 3+  1  4  3 -3 -7  3
Curve Equation t Generators 17856b1 [0,0,0,-492,-4208] 1 [26:24:1]
17856c (1 curve)	1	2+ 3+ 31+	2+ 3+ -1  0 -3  1  3 -1
Curve Equation t Generators 17856c1 [0,0,0,-108,-27216] 1 [45:243:1]
17856d (1 curve)	1	2+ 3+ 31+	2+ 3+ -1  4 -3 -3  7  3
Curve Equation t Generators 17856d1 [0,0,0,-4428,113616] 1 [48:108:1]
17856e (2 curves)	0	2+ 3+ 31-	2+ 3+  0  0  4 -2 -6 -4
Curve Equation t 17856e1 [0,0,0,-1080,13608] 2 17856e2 [0,0,0,-540,27216] 2
17856f (2 curves)	0	2+ 3+ 31-	2+ 3+  0  0 -4 -2  6 -4
Curve Equation t 17856f1 [0,0,0,-120,-504] 2 17856f2 [0,0,0,-60,-1008] 2
17856g (1 curve)	2	2+ 3+ 31-	2+ 3+  1 -4 -3 -3 -7 -3
Curve Equation t Generators 17856g1 [0,0,0,-492,4208] 1 [-2:72:1]&[4:48:1]
17856h (1 curve)	0	2+ 3+ 31-	2+ 3+ -1 -4  3 -3  7 -3
Curve Equation t 17856h1 [0,0,0,-4428,-113616] 1
17856i (2 curves)	0	2+ 3+ 31-	2+ 3+  3 -4  3 -5 -3  7
Curve Equation t 17856i1 [0,0,0,2964,113072] 1 17856i2 [0,0,0,-27756,-3814992] 1
17856j (2 curves)	2	2+ 3+ 31-	2+ 3+ -3 -4 -3 -5  3  7
Curve Equation t Generators 17856j1 [0,0,0,-3084,141296] 1 [-56:372:1]&[-2:384:1] 17856j2 [0,0,0,26676,-3052944] 1 [168:2484:1]&[238:4096:1]
17856k (1 curve)	0	2+ 3- 31+	2+ 3-  1  3  6  4  0  5
Curve Equation t 17856k1 [0,0,0,-612,5832] 1
17856l (1 curve)	0	2+ 3- 31+	2+ 3-  1 -3 -2  2  6 -1
Curve Equation t 17856l1 [0,0,0,-12,-232] 1
17856m (1 curve)	0	2+ 3- 31+	2+ 3- -1  1  0  6  0  3
Curve Equation t 17856m1 [0,0,0,132,376] 1
17856n (1 curve)	0	2+ 3- 31+	2+ 3- -1  2  1 -1 -3  1
Curve Equation t 17856n1 [0,0,0,-72588,7763024] 1
17856o (1 curve)	0	2+ 3- 31+	2+ 3- -1 -3 -4  2  0 -1
Curve Equation t 17856o1 [0,0,0,-3468,-78856] 1
17856p (2 curves)	0	2+ 3- 31+	2+ 3-  2  0  2 -4 -6 -4
Curve Equation t 17856p1 [0,0,0,276,560] 2 17856p2 [0,0,0,-1164,4592] 2
17856q (4 curves)	0	2+ 3- 31+	2+ 3- -2  0  0 -2  6 -4
Curve Equation t 17856q1 [0,0,0,-396,-15120] 2 17856q2 [0,0,0,-11916,-498960] 4 17856q3 [0,0,0,-190476,-31996944] 2 17856q4 [0,0,0,-17676,33264] 2
17856r (4 curves)	0	2+ 3- 31+	2+ 3- -2  0  4  2 -6 -4
Curve Equation t 17856r1 [0,0,0,-10056,388136] 2 17856r2 [0,0,0,-10236,373520] 4 17856r3 [0,0,0,-32556,-1813840] 2 17856r4 [0,0,0,9204,1625456] 2
17856s (2 curves)	0	2+ 3- 31+	2+ 3- -2  4  0 -6 -4  0
Curve Equation t 17856s1 [0,0,0,-291,-1100] 2 17856s2 [0,0,0,924,-7904] 2
17856t (1 curve)	0	2+ 3- 31+	2+ 3-  3 -2  5  7  1 -7
Curve Equation t 17856t1 [0,0,0,-9516,364592] 1
17856u (1 curve)	0	2+ 3- 31+	2+ 3-  3  5  4  2  8 -1
Curve Equation t 17856u1 [0,0,0,33684,5513848] 1
17856v (1 curve)	2	2+ 3- 31+	2+ 3- -3  2 -5 -1 -1 -7
Curve Equation t Generators 17856v1 [0,0,0,-1164,20464] 1 [-34:144:1]&[-19:189:1]
17856w (1 curve)	2	2+ 3- 31+	2+ 3- -3 -2 -1  1 -7 -5
Curve Equation t Generators 17856w1 [0,0,0,276,-1424] 1 [5:9:1]&[14:72:1]
17856x (1 curve)	0	2+ 3- 31+	2+ 3- -3 -5  2  4  4  5
Curve Equation t 17856x1 [0,0,0,-84,-2104] 1
17856y (2 curves)	1	2+ 3- 31-	2+ 3-  1 -2 -3  1 -3  5
Curve Equation t Generators 17856y1 [0,0,0,8628,-107152] 1 [14:128:1] 17856y2 [0,0,0,-803532,277375088] 1 [494:992:1]
17856z (1 curve)	1	2+ 3- 31-	2+ 3-  1 -3 -2 -4  4  7
Curve Equation t Generators 17856z1 [0,0,0,-5052,-152552] 1 [389:7533:1]
17856ba (1 curve)	1	2+ 3- 31-	2+ 3- -1 -1  0  6  8 -7
Curve Equation t Generators 17856ba1 [0,0,0,-228,-1496] 1 [149:1809:1]
17856bb (1 curve)	1	2+ 3- 31-	2+ 3- -1  2  3 -3 -1 -7
Curve Equation t Generators 17856bb1 [0,0,0,-48108,4620976] 1 [221:2187:1]
17856bc (1 curve)	1	2+ 3- 31-	2+ 3- -1 -2 -1 -1 -3 -1
Curve Equation t Generators 17856bc1 [0,0,0,-72588,-7763024] 1 [461:7533:1]
17856bd (2 curves)	1	2+ 3- 31-	2+ 3- -2  4  0 -2  0 -4
Curve Equation t Generators 17856bd1 [0,0,0,-336,-3256] 2 [25:63:1] 17856bd2 [0,0,0,-5916,-175120] 2 [397:7749:1]
17856be (2 curves)	1	2+ 3- 31-	2+ 3- -2 -4  0 -6 -4  0
Curve Equation t Generators 17856be1 [0,0,0,-291,1100] 2 [-8:54:1] 17856be2 [0,0,0,924,7904] 2 [4:108:1]
17856bf (2 curves)	1	2+ 3- 31-	2+ 3-  3 -1  0 -2  0  1
Curve Equation t Generators 17856bf1 [0,0,0,-109956,14754728] 1 [18545:163323:125] 17856bf2 [0,0,0,-9032916,10449369128] 1 [216905:279:125]
17856bg (1 curve)	1	2+ 3- 31-	2+ 3- -3  1 -6  0  4  3
Curve Equation t Generators 17856bg1 [0,0,0,276,-18664] 1 [109:1143:1]
17856bh (2 curves)	1	2+ 3- 31-	2+ 3- -3 -1 -6 -2 -6  1
Curve Equation t Generators 17856bh1 [0,0,0,-84,-376] 1 [13:27:1] 17856bh2 [0,0,0,636,3656] 1 [37:279:1]
17856bi (1 curve)	1	2+ 3- 31-	2+ 3- -3  2  1  1 -7  5
Curve Equation t Generators 17856bi1 [0,0,0,276,1424] 1 [10:72:1]
17856bj (1 curve)	1	2+ 3- 31-	2+ 3- -3 -3  2  4  0 -1
Curve Equation t Generators 17856bj1 [0,0,0,36,216] 1 [-3:9:1]
17856bk (2 curves)	0	2- 3+ 31+	2- 3+  0  0  4 -2  6  4
Curve Equation t 17856bk1 [0,0,0,-120,504] 2 17856bk2 [0,0,0,-60,1008] 2
17856bl (2 curves)	0	2- 3+ 31+	2- 3+  0  0 -4 -2 -6  4
Curve Equation t 17856bl1 [0,0,0,-1080,-13608] 2 17856bl2 [0,0,0,-540,-27216] 2
17856bm (2 curves)	0	2- 3+ 31+	2- 3+  3  4 -3 -5 -3 -7
Curve Equation t 17856bm1 [0,0,0,2964,-113072] 1 17856bm2 [0,0,0,-27756,3814992] 1
17856bn (2 curves)	0	2- 3+ 31+	2- 3+ -3  4  3 -5  3 -7
Curve Equation t 17856bn1 [0,0,0,-3084,-141296] 1 17856bn2 [0,0,0,26676,3052944] 1
17856bo (1 curve)	1	2- 3+ 31-	2- 3+  1  0 -3  1 -3  1
Curve Equation t Generators 17856bo1 [0,0,0,-12,-1008] 1 [12:24:1]
17856bp (1 curve)	1	2- 3+ 31-	2- 3+ -1  0  3  1  3  1
Curve Equation t Generators 17856bp1 [0,0,0,-108,27216] 1 [90:864:1]
17856bq (2 curves)	1	2- 3- 31+	2- 3-  1  2  3  1 -3 -5
Curve Equation t Generators 17856bq1 [0,0,0,8628,107152] 1 [92:1296:1] 17856bq2 [0,0,0,-803532,-277375088] 1 [475180:28395216:125]
17856br (1 curve)	1	2- 3- 31+	2- 3-  1  3  2 -4  4 -7
Curve Equation t Generators 17856br1 [0,0,0,-5052,152552] 1 [-83:9:1]
17856bs (1 curve)	1	2- 3- 31+	2- 3- -1  1  0  6  8  7
Curve Equation t Generators 17856bs1 [0,0,0,-228,1496] 1 [13:27:1]
17856bt (1 curve)	1	2- 3- 31+	2- 3- -1 -2 -3 -3 -1  7
Curve Equation t Generators 17856bt1 [0,0,0,-48108,-4620976] 1 [442:7776:1]
17856bu (2 curves)	1	2- 3- 31+	2- 3- -2 -4  0 -2  0  4
Curve Equation t Generators 17856bu1 [0,0,0,-336,3256] 2 [9:31:1] 17856bu2 [0,0,0,-5916,175120] 2 [38:72:1]
17856bv (2 curves)	1	2- 3- 31+	2- 3-  3  1  0 -2  0 -1
Curve Equation t Generators 17856bv1 [0,0,0,-109956,-14754728] 1 [1030510956055297:25022253254176071:1356204441509] 17856bv2 [0,0,0,-9032916,-10449369128] 1 [13588603334313384363263762638607051972263058065:2108276760355719603124349237292895421428057631529:555579759219242883768704427656857208577125]
17856bw (2 curves)	1	2- 3- 31+	2- 3- -3  1  6 -2 -6 -1
Curve Equation t Generators 17856bw1 [0,0,0,-84,376] 1 [5:9:1] 17856bw2 [0,0,0,636,-3656] 1 [53:423:1]
17856bx (1 curve)	1	2- 3- 31+	2- 3- -3 -1  6  0  4 -3
Curve Equation t Generators 17856bx1 [0,0,0,276,18664] 1 [-19:81:1]
17856by (1 curve)	1	2- 3- 31+	2- 3- -3  3 -2  4  0  1
Curve Equation t Generators 17856by1 [0,0,0,36,-216] 1 [21:99:1]
17856bz (1 curve)	0	2- 3- 31-	2- 3-  1  3  2  2  6  1
Curve Equation t 17856bz1 [0,0,0,-12,232] 1
17856ca (1 curve)	0	2- 3- 31-	2- 3-  1 -3 -6  4  0 -5
Curve Equation t 17856ca1 [0,0,0,-612,-5832] 1
17856cb (1 curve)	0	2- 3- 31-	2- 3- -1 -1  0  6  0 -3
Curve Equation t 17856cb1 [0,0,0,132,-376] 1
17856cc (1 curve)	0	2- 3- 31-	2- 3- -1  3  4  2  0  1
Curve Equation t 17856cc1 [0,0,0,-3468,78856] 1
17856cd (2 curves)	0	2- 3- 31-	2- 3-  2  0 -2 -4 -6  4
Curve Equation t 17856cd1 [0,0,0,276,-560] 2 17856cd2 [0,0,0,-1164,-4592] 2
17856ce (4 curves)	0	2- 3- 31-	2- 3- -2  0  0 -2  6  4
Curve Equation t 17856ce1 [0,0,0,-396,15120] 2 17856ce2 [0,0,0,-11916,498960] 4 17856ce3 [0,0,0,-17676,-33264] 2 17856ce4 [0,0,0,-190476,31996944] 2
17856cf (4 curves)	0	2- 3- 31-	2- 3- -2  0 -4  2 -6  4
Curve Equation t 17856cf1 [0,0,0,-10056,-388136] 2 17856cf2 [0,0,0,-10236,-373520] 4 17856cf3 [0,0,0,-32556,1813840] 2 17856cf4 [0,0,0,9204,-1625456] 2
17856cg (1 curve)	0	2- 3- 31-	2- 3-  3  2 -5  7  1  7
Curve Equation t 17856cg1 [0,0,0,-9516,-364592] 1
17856ch (1 curve)	0	2- 3- 31-	2- 3-  3 -5 -4  2  8  1
Curve Equation t 17856ch1 [0,0,0,33684,-5513848] 1
17856ci (1 curve)	0	2- 3- 31-	2- 3- -3 -2  5 -1 -1  7
Curve Equation t 17856ci1 [0,0,0,-1164,-20464] 1
17856cj (1 curve)	0	2- 3- 31-	2- 3- -3  5 -2  4  4 -5
Curve Equation t 17856cj1 [0,0,0,-84,2104] 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
Back to Tables and computations