Elliptic curves over $\Q$ of conductor 966

Results (27 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
966.a1	966d2	966.a	966d	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2 \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.6	2B	$184$	$12$	$0$	$0.197258770$	$1$		$10$	$384$	$0.103040$	$42180533641/22862322$	$[1, 1, 0, -72, -90]$	\(y^2+xy=x^3+x^2-72x-90\)	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?
966.a2	966d1	966.a	966d	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{2} \cdot 3^{4} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.1	2B	$184$	$12$	$0$	$0.394517540$	$1$		$11$	$192$	$-0.243533$	$590589719/365148$	$[1, 1, 0, 18, 0]$	\(y^2+xy=x^3+x^2+18x\)	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?
966.b1	966a2	966.b	966a	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{5} \cdot 3^{8} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1288$	$12$	$0$	$1.650614271$	$1$		$6$	$1920$	$0.982336$	$4144806984356137/568114785504$	$[1, 1, 0, -3346, 63700]$	\(y^2+xy=x^3+x^2-3346x+63700\)	2.3.0.a.1, 28.6.0.c.1, 184.6.0.?, 1288.12.0.?
966.b2	966a1	966.b	966a	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{3} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1288$	$12$	$0$	$0.825307135$	$1$		$9$	$960$	$0.635762$	$4101378352343/15049939968$	$[1, 1, 0, 334, 5556]$	\(y^2+xy=x^3+x^2+334x+5556\)	2.3.0.a.1, 14.6.0.b.1, 184.6.0.?, 1288.12.0.?
966.c1	966c2	966.c	966c	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{16} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1288$	$12$	$0$	$3.116373404$	$1$		$4$	$8448$	$1.749481$	$1733490909744055732873/99355964553216$	$[1, 1, 0, -250264, 48082240]$	\(y^2+xy=x^3+x^2-250264x+48082240\)	2.3.0.a.1, 28.6.0.c.1, 184.6.0.?, 1288.12.0.?
966.c2	966c1	966.c	966c	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{22} \cdot 3^{8} \cdot 7 \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1288$	$12$	$0$	$1.558186702$	$1$		$7$	$4224$	$1.402908$	$-354499561600764553/101902222098432$	$[1, 1, 0, -14744, 836928]$	\(y^2+xy=x^3+x^2-14744x+836928\)	2.3.0.a.1, 14.6.0.b.1, 184.6.0.?, 1288.12.0.?
966.d1	966b1	966.d	966b	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{13} \cdot 3^{3} \cdot 7^{5} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3864$	$2$	$0$	$1$	$1$		$0$	$1560$	$0.939403$	$-14943832855786297/85501108224$	$[1, 1, 0, -5131, -144323]$	\(y^2+xy=x^3+x^2-5131x-144323\)	3864.2.0.?
966.e1	966e2	966.e	966e	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{3} \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.6	2B	$184$	$12$	$0$	$0.541574832$	$1$		$6$	$384$	$0.323846$	$5182207647625/91449288$	$[1, 0, 1, -361, 2564]$	\(y^2+xy+y=x^3-361x+2564\)	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?
966.e2	966e1	966.e	966e	$2$	$2$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{6} \cdot 3^{4} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.1	2B	$184$	$12$	$0$	$0.270787416$	$1$		$11$	$192$	$-0.022728$	$-15625/5842368$	$[1, 0, 1, -1, 116]$	\(y^2+xy+y=x^3-x+116\)	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?
966.f1	966f4	966.f	966f	$4$	$6$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{15} \cdot 3^{2} \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.8.0.2	2B, 3B.1.2	$552$	$96$	$1$	$1$	$1$		$0$	$28800$	$2.360363$	$385693937170561837203625/2159357734550274048$	$[1, 0, 1, -1516491, -715440266]$	\(y^2+xy+y=x^3-1516491x-715440266\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.b.1, 24.48.0-24.y.1.13, $\ldots$
966.f2	966f2	966.f	966f	$4$	$6$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{5} \cdot 3^{6} \cdot 7^{4} \cdot 23^{6} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.8.0.1	2B, 3B.1.1	$552$	$96$	$1$	$1$	$1$		$4$	$9600$	$1.811056$	$155355156733986861625/8291568305839392$	$[1, 0, 1, -111996, 13735450]$	\(y^2+xy+y=x^3-111996x+13735450\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.b.1, 24.48.0-24.y.1.15, $\ldots$
966.f3	966f3	966.f	966f	$4$	$6$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{30} \cdot 3^{4} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.8.0.2	2B, 3B.1.2	$552$	$96$	$1$	$1$	$1$		$1$	$14400$	$2.013790$	$-8152944444844179625/235342826399858688$	$[1, 0, 1, -41931, -23576714]$	\(y^2+xy+y=x^3-41931x-23576714\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.c.1, 24.48.0-24.bw.1.11, $\ldots$
966.f4	966f1	966.f	966f	$4$	$6$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{12} \cdot 7^{2} \cdot 23^{3} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.8.0.1	2B, 3B.1.1	$552$	$96$	$1$	$1$	$1$		$5$	$4800$	$1.464481$	$11079872671250375/324440155855872$	$[1, 0, 1, 4644, 858394]$	\(y^2+xy+y=x^3+4644x+858394\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.c.1, 24.48.0-24.bw.1.15, $\ldots$
966.g1	966g5	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{16} \cdot 7 \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.48	2B	$2576$	$192$	$1$	$4.858093228$	$1$		$0$	$4096$	$1.415974$	$54804145548726848737/637608031452$	$[1, 1, 1, -79134, -8601153]$	\(y^2+xy+y=x^3+x^2-79134x-8601153\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 28.24.0-28.h.1.1, $\ldots$
966.g2	966g4	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.159	2B	$2576$	$192$	$1$	$2.429046614$	$1$		$12$	$2048$	$1.069401$	$614716917569296417/19093020912$	$[1, 1, 1, -17714, 900047]$	\(y^2+xy+y=x^3+x^2-17714x+900047\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 92.24.0.?, 112.96.0.?, $\ldots$
966.g3	966g3	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 7^{2} \cdot 23^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.34	2Cs	$1288$	$192$	$1$	$2.429046614$	$1$		$6$	$2048$	$1.069401$	$14447092394873377/1439452851984$	$[1, 1, 1, -5074, -128689]$	\(y^2+xy+y=x^3+x^2-5074x-128689\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 28.48.0-28.c.1.3, 56.96.0-56.j.2.5, $\ldots$
966.g4	966g2	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{8} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.24	2Cs	$1288$	$192$	$1$	$1.214523307$	$1$		$18$	$1024$	$0.722827$	$169967019783457/26337394944$	$[1, 1, 1, -1154, 12431]$	\(y^2+xy+y=x^3+x^2-1154x+12431\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 56.96.0-56.v.2.6, 92.48.0.?, $\ldots$
966.g5	966g1	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{16} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.27	2B	$2576$	$192$	$1$	$0.607261653$	$1$		$17$	$512$	$0.376254$	$221115865823/664731648$	$[1, 1, 1, 126, 1167]$	\(y^2+xy+y=x^3+x^2+126x+1167\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.e.1.2, 46.6.0.a.1, $\ldots$
966.g6	966g6	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{2} \cdot 3^{4} \cdot 7 \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.177	2B	$2576$	$192$	$1$	$4.858093228$	$1$		$2$	$4096$	$1.415974$	$27207619911317663/177609314617308$	$[1, 1, 1, 6266, -609505]$	\(y^2+xy+y=x^3+x^2+6266x-609505\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 14.6.0.b.1, 28.24.0-28.g.1.1, $\ldots$
966.h1	966h1	966.h	966h	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{5} \cdot 3^{9} \cdot 7 \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3864$	$2$	$0$	$1$	$1$		$0$	$360$	$0.393778$	$-25727239787761/101406816$	$[1, 1, 1, -615, -6147]$	\(y^2+xy+y=x^3+x^2-615x-6147\)	3864.2.0.?
966.i1	966k2	966.i	966k	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2 \cdot 3 \cdot 7^{3} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$3864$	$16$	$0$	$1$	$1$		$0$	$360$	$0.101601$	$-2181825073/25039686$	$[1, 0, 0, -27, -249]$	\(y^2+xy=x^3-27x-249\)	3.8.0-3.a.1.1, 3864.16.0.?
966.i2	966k1	966.i	966k	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{3} \cdot 3^{3} \cdot 7 \cdot 23 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$3864$	$16$	$0$	$1$	$1$		$2$	$120$	$-0.447706$	$2924207/34776$	$[1, 0, 0, 3, 9]$	\(y^2+xy=x^3+3x+9\)	3.8.0-3.a.1.2, 3864.16.0.?
966.j1	966i3	966.j	966i	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2 \cdot 3^{6} \cdot 7^{4} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$1288$	$48$	$0$	$1$	$4$	$2$	$0$	$3840$	$1.376987$	$632678989847546725777/80515134$	$[1, 0, 0, -178849, -29127301]$	\(y^2+xy=x^3-178849x-29127301\)	2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 184.24.0.?, 1288.48.0.?
966.j2	966i4	966.j	966i	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2 \cdot 3^{24} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$1288$	$48$	$0$	$1$	$1$		$0$	$3840$	$1.376987$	$231331938231569617/90942310746882$	$[1, 0, 0, -12789, -316305]$	\(y^2+xy=x^3-12789x-316305\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 56.24.0-56.z.1.10, $\ldots$
966.j3	966i2	966.j	966i	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1288$	$48$	$0$	$1$	$1$		$2$	$1920$	$1.030415$	$154502321244119857/55101928644$	$[1, 0, 0, -11179, -455731]$	\(y^2+xy=x^3-11179x-455731\)	2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.1, 184.24.0.?, 1288.48.0.?
966.j4	966i1	966.j	966i	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 7 \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1288$	$48$	$0$	$1$	$1$		$3$	$960$	$0.683841$	$-23771111713777/22848457968$	$[1, 0, 0, -599, -9255]$	\(y^2+xy=x^3-599x-9255\)	2.3.0.a.1, 4.12.0-4.c.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, 184.24.0.?, $\ldots$
966.k1	966j1	966.k	966j	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{9} \cdot 3 \cdot 7^{11} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3864$	$2$	$0$	$1$	$1$		$0$	$3960$	$1.344131$	$83228502970940543/69854999176704$	$[1, 0, 0, 9096, 224832]$	\(y^2+xy=x^3+9096x+224832\)	3864.2.0.?