Elliptic curves over $\Q$ of conductor 23064

Results (24 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	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
23064.a1	23064c1	23064.a	23064c	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{8} \cdot 31^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$122880$	$1.646212$	$3114752/203391$	$0.96293$	$4.28480$	$[0, -1, 0, 7368, -2576619]$	\(y^2=x^3-x^2+7368x-2576619\)	62.2.0.a.1	$[]$
23064.b1	23064b4	23064.b	23064b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{10} \cdot 3^{12} \cdot 31^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$744$	$48$	$0$	$1$	$1$		$1$	$460800$	$2.394665$	$79874724388/16474671$	$0.95751$	$5.23979$	$[0, -1, 0, -869064, -249877476]$	\(y^2=x^3-x^2-869064x-249877476\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.z.1.1, 124.24.0.?, 744.48.0.?	$[]$
23064.b2	23064b2	23064.b	23064b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 31^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$372$	$48$	$0$	$1$	$1$		$3$	$230400$	$2.048088$	$9930407632/700569$	$0.91892$	$4.89427$	$[0, -1, 0, -273244, 51607444]$	\(y^2=x^3-x^2-273244x+51607444\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.3, 124.24.0.?, 372.48.0.?	$[]$
23064.b3	23064b1	23064.b	23064b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{4} \cdot 3^{3} \cdot 31^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$744$	$48$	$0$	$1$	$1$		$3$	$115200$	$1.701515$	$150651000832/837$	$0.97851$	$4.88897$	$[0, -1, 0, -268439, 53621700]$	\(y^2=x^3-x^2-268439x+53621700\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.9, 186.6.0.?, 248.24.0.?, $\ldots$	$[]$
23064.b4	23064b3	23064.b	23064b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{10} \cdot 3^{3} \cdot 31^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$744$	$48$	$0$	$1$	$1$		$1$	$460800$	$2.394665$	$1804870652/24935067$	$0.98732$	$5.17410$	$[0, -1, 0, 245696, 224103100]$	\(y^2=x^3-x^2+245696x+224103100\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.12.0-4.c.1.5, 12.12.0.g.1, $\ldots$	$[]$
23064.c1	23064h1	23064.c	23064h	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 31^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1.775086099$	$1$		$0$	$92160$	$1.644304$	$-6179217664/22599$	$1.06589$	$4.57168$	$[0, -1, 0, -92576, -10845063]$	\(y^2=x^3-x^2-92576x-10845063\)	62.2.0.a.1	$[(1541/2, 25947/2)]$
23064.d1	23064a1	23064.d	23064a	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{11} \cdot 3 \cdot 31^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$24$	$2$	$0$	$31.77315673$	$1$		$0$	$193440$	$1.747427$	$-21266/3$	$0.79636$	$4.50721$	$[0, -1, 0, -69512, -7843860]$	\(y^2=x^3-x^2-69512x-7843860\)	24.2.0.b.1	$[(41879845747249/367751, 23859749567894890330/367751)]$
23064.e1	23064i1	23064.e	23064i	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 31^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$30$	$30$	$1$	$4.358615675$	$1$		$2$	$28800$	$1.087152$	$155958272/14348907$	$1.10208$	$3.61742$	$[0, -1, 0, 703, 89877]$	\(y^2=x^3-x^2+703x+89877\)	5.5.0.a.1, 6.6.0.b.1, 30.30.1.a.1	$[(123, 1422)]$
23064.f1	23064j1	23064.f	23064j	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$0.731749225$	$1$		$4$	$6144$	$0.328311$	$1257728/729$	$1.22690$	$2.69951$	$[0, -1, 0, 176, -23]$	\(y^2=x^3-x^2+176x-23\)	62.2.0.a.1	$[(4, 27)]$
23064.g1	23064d1	23064.g	23064d	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 31^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$6$	$0$	$1$	$1$		$0$	$5760$	$0.006682$	$-31744/27$	$0.80977$	$2.35742$	$[0, -1, 0, -41, -147]$	\(y^2=x^3-x^2-41x-147\)	6.6.0.b.1	$[]$
23064.h1	23064p1	23064.h	23064p	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{11} \cdot 3^{3} \cdot 31^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$744$	$2$	$0$	$1$	$1$		$0$	$138240$	$1.619638$	$-1825346/837$	$0.84390$	$4.30313$	$[0, 1, 0, -31072, 2812064]$	\(y^2=x^3+x^2-31072x+2812064\)	744.2.0.?	$[]$
23064.i1	23064m6	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.210	2B	$1488$	$192$	$1$	$1$	$1$		$1$	$115200$	$1.764788$	$3065617154/9$	$1.21059$	$4.98426$	$[0, 1, 0, -369344, 86272992]$	\(y^2=x^3+x^2-369344x+86272992\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.r.1, 16.48.0.l.1, 24.48.0.bf.1, $\ldots$	$[]$
23064.i2	23064m4	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{10} \cdot 3 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.127	2B	$1488$	$192$	$1$	$1$	$4$	$2$	$1$	$57600$	$1.418215$	$28756228/3$	$1.05617$	$4.45049$	$[0, 1, 0, -61824, -5936880]$	\(y^2=x^3+x^2-61824x-5936880\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0.h.1, 16.48.0.bb.2, $\ldots$	$[]$
23064.i3	23064m3	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 31^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.88	2Cs	$744$	$192$	$1$	$1$	$1$		$3$	$57600$	$1.418215$	$1556068/81$	$1.03212$	$4.16016$	$[0, 1, 0, -23384, 1305216]$	\(y^2=x^3+x^2-23384x+1305216\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 124.24.0.?, $\ldots$	$[]$
23064.i4	23064m2	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 31^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.138	2Cs	$744$	$192$	$1$	$1$	$1$		$3$	$28800$	$1.071642$	$35152/9$	$0.97255$	$3.64488$	$[0, 1, 0, -4164, -78624]$	\(y^2=x^3+x^2-4164x-78624\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.h.1, 12.24.0.c.1, 24.96.1.bu.1, $\ldots$	$[]$
23064.i5	23064m1	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.150	2B	$1488$	$192$	$1$	$1$	$1$		$1$	$14400$	$0.725068$	$2048/3$	$1.17572$	$3.12832$	$[0, 1, 0, 641, -7510]$	\(y^2=x^3+x^2+641x-7510\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.ba.1, 12.12.0.g.1, $\ldots$	$[]$
23064.i6	23064m5	23064.i	23064m	$6$	$8$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{11} \cdot 3^{8} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.218	2B	$1488$	$192$	$1$	$1$	$1$		$1$	$115200$	$1.764788$	$207646/6561$	$1.15980$	$4.42500$	$[0, 1, 0, 15056, 5210720]$	\(y^2=x^3+x^2+15056x+5210720\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 124.12.0.?, $\ldots$	$[]$
23064.j1	23064f1	23064.j	23064f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 31^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$0.805529147$	$1$		$2$	$30720$	$1.105099$	$340736/279$	$0.77804$	$3.59499$	$[0, 1, 0, 3524, 53033]$	\(y^2=x^3+x^2+3524x+53033\)	62.2.0.a.1	$[(196, 2883)]$
23064.k1	23064l1	23064.k	23064l	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{4} \cdot 31^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$184320$	$1.906748$	$-19102326016/2413071$	$0.93313$	$4.70306$	$[0, 1, 0, -134860, -21085123]$	\(y^2=x^3+x^2-134860x-21085123\)	62.2.0.a.1	$[]$
23064.l1	23064g1	23064.l	23064g	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{11} \cdot 3 \cdot 31^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$24$	$2$	$0$	$2.509589246$	$1$		$2$	$6240$	$0.030433$	$-21266/3$	$0.79636$	$2.45625$	$[0, 1, 0, -72, 240]$	\(y^2=x^3+x^2-72x+240\)	24.2.0.b.1	$[(11, 30)]$
23064.m1	23064k1	23064.m	23064k	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 31^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.5.0.1	5S4	$30$	$30$	$1$	$3.534918214$	$1$		$2$	$892800$	$2.804146$	$155958272/14348907$	$1.10208$	$5.66838$	$[0, 1, 0, 675263, -2684279437]$	\(y^2=x^3+x^2+675263x-2684279437\)	5.5.0.a.1, 6.6.0.b.1, 30.30.1.a.1	$[(3197, 179334)]$
23064.n1	23064n1	23064.n	23064n	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 31^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$190464$	$2.045303$	$1257728/729$	$1.22690$	$4.75046$	$[0, 1, 0, 168816, -1004067]$	\(y^2=x^3+x^2+168816x-1004067\)	62.2.0.a.1	$[]$
23064.o1	23064o1	23064.o	23064o	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 31^{11} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$1382400$	$2.611042$	$5661965297408/20870651079$	$1.01686$	$5.41727$	$[0, 1, 0, 899176, 760776789]$	\(y^2=x^3+x^2+899176x+760776789\)	62.2.0.a.1	$[]$
23064.p1	23064e1	23064.p	23064e	$1$	$1$	\( 2^{3} \cdot 3 \cdot 31^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 31^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$6$	$0$	$1$	$1$		$0$	$178560$	$1.723677$	$-31744/27$	$0.80977$	$4.40837$	$[0, 1, 0, -39721, 4775387]$	\(y^2=x^3+x^2-39721x+4775387\)	6.6.0.b.1	$[]$