Cremona's table of elliptic curves

31824 = 2⁴ · 3² · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
31824a (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  0  2  6 13+ 17+  8
Curve Equation t 31824a1 [0,0,0,-90,-81] 2 31824a2 [0,0,0,-855,9558] 2
31824b (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  0 -2 -2 13+ 17+  4
Curve Equation t 31824b1 [0,0,0,-1194015,-502183874] 2 31824b2 [0,0,0,-1196355,-500116718] 2
31824c (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  0 -2 -2 13+ 17+  4
Curve Equation t 31824c1 [0,0,0,-360975,-82071538] 2 31824c2 [0,0,0,-756435,129974114] 2
31824d (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  0 -2 -2 13+ 17+  4
Curve Equation t 31824d1 [0,0,0,-7050,-224773] 2 31824d2 [0,0,0,-13935,286094] 2
31824e (2 curves)	2	2+ 3- 13+ 17+	2+ 3-  0 -2 -6 13+ 17+  0
Curve Equation t Generators 31824e1 [0,0,0,-615,-4826] 2 [-15:32:1]&[-10:18:1] 31824e2 [0,0,0,-2955,57418] 2 [-43:324:1]&[-13:306:1]
31824f (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  0  4 -2 13+ 17+ -8
Curve Equation t 31824f1 [0,0,0,-3990,349859] 2 31824f2 [0,0,0,-102855,12668438] 2
31824g (2 curves)	0	2+ 3- 13+ 17+	2+ 3- -2 -2 -2 13+ 17+  8
Curve Equation t 31824g1 [0,0,0,-12711,-493594] 2 31824g2 [0,0,0,17709,-2495230] 2
31824h (2 curves)	0	2+ 3- 13+ 17+	2+ 3-  4 -2 -2 13+ 17+  0
Curve Equation t 31824h1 [0,0,0,-498,3175] 2 31824h2 [0,0,0,-7383,244150] 2
31824i (2 curves)	2	2+ 3- 13+ 17+	2+ 3- -4 -2 -2 13+ 17+ -4
Curve Equation t Generators 31824i1 [0,0,0,-207,270] 2 [-6:36:1]&[-2:26:1] 31824i2 [0,0,0,-2547,49410] 2 [33:-36:1]&[-45:270:1]
31824j (2 curves)	1	2+ 3- 13+ 17-	2+ 3-  0 -2  4 13+ 17-  4
Curve Equation t Generators 31824j1 [0,0,0,-128595,17687842] 2 [-141:5746:1] 31824j2 [0,0,0,-67755,34467514] 2 [473:-10404:1]
31824k (2 curves)	1	2+ 3- 13+ 17-	2+ 3-  2 -4  6 13+ 17- -8
Curve Equation t Generators 31824k1 [0,0,0,-3819,-88598] 2 [-39:32:1] 31824k2 [0,0,0,861,-291710] 2 [78:500:1]
31824l (2 curves)	1	2+ 3- 13+ 17-	2+ 3- -2 -2  4 13+ 17- -4
Curve Equation t Generators 31824l1 [0,0,0,-15051,709706] 2 [91:-306:1] 31824l2 [0,0,0,-19731,231410] 2 [7:306:1]
31824m (2 curves)	1	2+ 3- 13- 17+	2+ 3-  2  2  0 13- 17+  0
Curve Equation t Generators 31824m1 [0,0,0,-5214,92207] 2 [-29:468:1] 31824m2 [0,0,0,15441,641630] 2 [170:2860:1]
31824n (4 curves)	1	2+ 3- 13- 17+	2+ 3-  2  4 -4 13- 17+  4
Curve Equation t Generators 31824n1 [0,0,0,-354,6775] 2 [27:130:1] 31824n2 [0,0,0,-7959,272950] 4 [197:2520:1] 31824n3 [0,0,0,-10299,99322] 2 [-79:648:1] 31824n4 [0,0,0,-127299,17481778] 2 [34570:231462:125]
31824o (4 curves)	1	2+ 3- 13- 17+	2+ 3- -2  0  4 13- 17+ -4
Curve Equation t Generators 31824o1 [0,0,0,-666,6615] 2 [159:1980:1] 31824o2 [0,0,0,-711,5670] 4 [-27:72:1] 31824o3 [0,0,0,1629,35154] 2 [-14:98:1] 31824o4 [0,0,0,-3771,-84294] 2 [-29:26:1]
31824p (2 curves)	1	2+ 3- 13- 17+	2+ 3- -2  2  4 13- 17+  8
Curve Equation t Generators 31824p1 [0,0,0,114,115] 2 [3:22:1] 31824p2 [0,0,0,-471,934] 2 [-15:68:1]
31824q (4 curves)	1	2+ 3- 13- 17+	2+ 3- -2  4  0 13- 17+ -4
Curve Equation t Generators 31824q1 [0,0,0,-4026,85399] 2 [82:1701:8] 31824q2 [0,0,0,-17031,-770330] 4 [5106:44954:27] 31824q3 [0,0,0,22749,-3833390] 2 [9284574:111950090:59319] 31824q4 [0,0,0,-264891,-52473926] 2 [755:13338:1]
31824r (2 curves)	1	2- 3- 13+ 17+	2- 3-  0  2 -2 13+ 17+  0
Curve Equation t Generators 31824r1 [0,0,0,-4755,-119662] 2 [-34:52:1] 31824r2 [0,0,0,-14115,496226] 2 [145:-1224:1]
31824s (2 curves)	1	2- 3- 13+ 17+	2- 3-  0  2 -2 13+ 17+  4
Curve Equation t Generators 31824s1 [0,0,0,-2955,31034] 2 [5:128:1] 31824s2 [0,0,0,-40395,3123578] 2 [37:1296:1]
31824t (2 curves)	1	2- 3- 13+ 17+	2- 3-  0  2 -2 13+ 17+  8
Curve Equation t Generators 31824t1 [0,0,0,-163875,23378722] 2 [174:364:1] 31824t2 [0,0,0,-2560035,1576569634] 2 [1073:8064:1]
31824u (2 curves)	1	2- 3- 13+ 17+	2- 3-  2  0  2 13+ 17+  2
Curve Equation t Generators 31824u1 [0,0,0,-6744,212807] 2 [-19:578:1] 31824u2 [0,0,0,-9039,55370] 2 [-206:4165:8]
31824v (2 curves)	1	2- 3- 13+ 17+	2- 3- -2 -2  2 13+ 17+  4
Curve Equation t Generators 31824v1 [0,0,0,-7851,-258086] 2 [119:702:1] 31824v2 [0,0,0,3669,-951590] 2 [1463:55998:1]
31824w (2 curves)	1	2- 3- 13+ 17+	2- 3- -2 -2 -6 13+ 17+ -4
Curve Equation t Generators 31824w1 [0,0,0,-8571,305386] 2 [45:104:1] 31824w2 [0,0,0,-7851,358810] 2 [47:-306:1]
31824x (2 curves)	1	2- 3- 13+ 17+	2- 3- -2  4  2 13+ 17+ -2
Curve Equation t Generators 31824x1 [0,0,0,-1416,18619] 2 [5:108:1] 31824x2 [0,0,0,-22071,1262050] 2 [2946:10556:27]
31824y (2 curves)	1	2- 3- 13+ 17+	2- 3-  4  2 -2 13+ 17+  0
Curve Equation t Generators 31824y1 [0,0,0,-24723,-877230] 2 [-430:4355:8] 31824y2 [0,0,0,-174483,27427410] 2 [345:2880:1]
31824z (2 curves)	1	2- 3- 13+ 17+	2- 3-  4 -2  6 13+ 17+ -4
Curve Equation t Generators 31824z1 [0,0,0,-37803,-2826470] 2 [2810:148590:1] 31824z2 [0,0,0,-47163,-1319510] 2 [-195:680:1]
31824ba (2 curves)	1	2- 3- 13+ 17+	2- 3- -4  2  6 13+ 17+ -8
Curve Equation t Generators 31824ba1 [0,0,0,-105507,13169250] 2 [201:288:1] 31824ba2 [0,0,0,-1687347,843635250] 2 [753:144:1]
31824bb (2 curves)	0	2- 3- 13+ 17-	2- 3-  0 -2 -4 13+ 17- -4
Curve Equation t 31824bb1 [0,0,0,-2751915,-1698391334] 2 31824bb2 [0,0,0,1141845,-6119366438] 2
31824bc (2 curves)	0	2- 3- 13+ 17-	2- 3-  2 -2 -2 13+ 17- -2
Curve Equation t 31824bc1 [0,0,0,-9084,239047] 2 31824bc2 [0,0,0,23721,1570930] 2
31824bd (2 curves)	0	2- 3- 13+ 17-	2- 3-  2 -2 -2 13+ 17-  6
Curve Equation t 31824bd1 [0,0,0,-11244,458903] 2 31824bd2 [0,0,0,-10839,493490] 2
31824be (2 curves)	0	2- 3- 13+ 17-	2- 3-  2 -2  4 13+ 17-  4
Curve Equation t 31824be1 [0,0,0,-1299,-15662] 2 31824be2 [0,0,0,-20019,-1090190] 2
31824bf (2 curves)	0	2- 3- 13+ 17-	2- 3-  2  4 -2 13+ 17-  0
Curve Equation t 31824bf1 [0,0,0,-254739,-17728558] 2 31824bf2 [0,0,0,943341,-136817710] 2
31824bg (2 curves)	2	2- 3- 13+ 17-	2- 3- -2 -4 -2 13+ 17-  0
Curve Equation t Generators 31824bg1 [0,0,0,-13491,583794] 2 [-105:918:1]&[-71:1088:1] 31824bg2 [0,0,0,5229,2077650] 2 [-111:360:1]&[-63:1224:1]
31824bh (2 curves)	0	2- 3- 13+ 17-	2- 3- -4  4 -2 13+ 17-  4
Curve Equation t 31824bh1 [0,0,0,-20872947,13099168690] 2 31824bh2 [0,0,0,-270073587,1706915918770] 2
31824bi (2 curves)	0	2- 3- 13- 17+	2- 3-  0  2  0 13- 17+  6
Curve Equation t 31824bi1 [0,0,0,-2640,49619] 2 31824bi2 [0,0,0,-41655,3272258] 2
31824bj (4 curves)	0	2- 3- 13- 17+	2- 3-  2  0  0 13- 17+  0
Curve Equation t 31824bj1 [0,0,0,1221,30058] 2 31824bj2 [0,0,0,-10299,336490] 4 31824bj3 [0,0,0,-47739,-3699542] 2 31824bj4 [0,0,0,-157179,23984170] 2
31824bk (6 curves)	0	2- 3- 13- 17+	2- 3-  2  0  4 13- 17+  4
Curve Equation t 31824bk1 [0,0,0,-77619,8323378] 2 31824bk2 [0,0,0,-78339,8161090] 4 31824bk3 [0,0,0,31821,29289778] 2 31824bk4 [0,0,0,-200019,-23354030] 4 31824bk5 [0,0,0,558141,-158154878] 2 31824bk6 [0,0,0,-2905059,-1905520862] 2
31824bl (2 curves)	1	2- 3- 13- 17-	2- 3-  0  0 -4 13- 17- -2
Curve Equation t Generators 31824bl1 [0,0,0,-300,-1757] 2 [197:2754:1] 31824bl2 [0,0,0,465,-9254] 2 [1570:22113:8]
31824bm (4 curves)	1	2- 3- 13- 17-	2- 3-  0  4  0 13- 17- -2
Curve Equation t Generators 31824bm1 [0,0,0,-28380,1840187] 2 [397:7290:1] 31824bm2 [0,0,0,-27615,1944074] 2 [-1338:48230:27] 31824bm3 [0,0,0,-44580,-489049] 2 [3457:202878:1] 31824bm4 [0,0,0,176505,-3893758] 2 [74:3094:1]

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