Elliptic curves over $\Q$ of conductor 32487

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (35 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
32487.a1	32487i1	32487.a	32487i	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 7^{7} \cdot 13^{3} \cdot 17^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.099161187$	$1$		$32$	$105984$	$1.111115$	$-325660672/40000779$	$[0, -1, 1, -702, 104852]$	\(y^2+y=x^3-x^2-702x+104852\)
32487.b1	32487g2	32487.b	32487g	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 7^{6} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.892332799$	$1$		$4$	$46080$	$1.102852$	$104154702625/24649677$	$[1, 1, 1, -4803, -100500]$	\(y^2+xy+y=x^3+x^2-4803x-100500\)
32487.b2	32487g1	32487.b	32487g	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.946166399$	$1$		$7$	$23040$	$0.756278$	$3981876625/232713$	$[1, 1, 1, -1618, 23078]$	\(y^2+xy+y=x^3+x^2-1618x+23078\)
32487.c1	32487b1	32487.c	32487b	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{5} \cdot 7^{7} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$107520$	$1.221601$	$10418796526321/6390657$	$[1, 1, 1, -22296, -1290024]$	\(y^2+xy+y=x^3+x^2-22296x-1290024\)
32487.c2	32487b2	32487.c	32487b	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{10} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$215040$	$1.568176$	$-5602762882081/8312741073$	$[1, 1, 1, -18131, -1781494]$	\(y^2+xy+y=x^3+x^2-18131x-1781494\)
32487.d1	32487n4	32487.d	32487n	$4$	$4$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3 \cdot 7^{7} \cdot 13 \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.415866576$	$1$		$0$	$245760$	$1.794897$	$1677087406638588673/4641$	$[1, 0, 0, -1212849, 514011504]$	\(y^2+xy=x^3-1212849x+514011504\)
32487.d2	32487n2	32487.d	32487n	$4$	$4$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{8} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2.207933288$	$1$		$6$	$122880$	$1.448324$	$409460675852593/21538881$	$[1, 0, 0, -75804, 8026479]$	\(y^2+xy=x^3-75804x+8026479\)
32487.d3	32487n3	32487.d	32487n	$4$	$4$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 7^{10} \cdot 13^{4} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.103966644$	$1$		$6$	$245760$	$1.794897$	$-345608484635233/94427721297$	$[1, 0, 0, -71639, 8948610]$	\(y^2+xy=x^3-71639x+8948610\)
32487.d4	32487n1	32487.d	32487n	$4$	$4$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3 \cdot 7^{7} \cdot 13 \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.415866576$	$1$		$1$	$61440$	$1.101751$	$117433042273/22801233$	$[1, 0, 0, -4999, 110480]$	\(y^2+xy=x^3-4999x+110480\)
32487.e1	32487m6	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{8} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$8.257050588$	$1$		$2$	$589824$	$2.354843$	$7389727131216686257/6115533215337$	$[1, 0, 0, -1988372, 1078244103]$	\(y^2+xy=x^3-1988372x+1078244103\)
32487.e2	32487m4	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{10} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$4.128525294$	$1$		$6$	$294912$	$2.008266$	$3275619238041697/1605271262049$	$[1, 0, 0, -151607, 8879520]$	\(y^2+xy=x^3-151607x+8879520\)
32487.e3	32487m2	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{8} \cdot 13^{2} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$8.257050588$	$1$		$2$	$147456$	$1.661695$	$495909170514577/6224736609$	$[1, 0, 0, -80802, -8750925]$	\(y^2+xy=x^3-80802x-8750925\)
32487.e4	32487m1	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3 \cdot 7^{7} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$16.51410117$	$1$		$1$	$73728$	$1.315121$	$491411892194497/78897$	$[1, 0, 0, -80557, -8807128]$	\(y^2+xy=x^3-80557x-8807128\)
32487.e5	32487m3	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3 \cdot 7^{7} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$16.51410117$	$1$		$0$	$294912$	$2.008266$	$-2533811507137/1904381781393$	$[1, 0, 0, -13917, -22783398]$	\(y^2+xy=x^3-13917x-22783398\)
32487.e6	32487m5	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 7^{14} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$2.064262647$	$1$		$2$	$589824$	$2.354843$	$158346567380527343/108665074944153$	$[1, 0, 0, 552278, 68146637]$	\(y^2+xy=x^3+552278x+68146637\)
32487.f1	32487l6	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{16} \cdot 7^{6} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$0.910669871$	$1$		$6$	$393216$	$2.128113$	$908031902324522977/161726530797$	$[1, 0, 0, -988527, 378154692]$	\(y^2+xy=x^3-988527x+378154692\)
32487.f2	32487l4	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 7^{6} \cdot 13^{2} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.13	2Cs	$1.821339742$	$1$		$8$	$196608$	$1.781538$	$296380748763217/92608836489$	$[1, 0, 0, -68062, 4629995]$	\(y^2+xy=x^3-68062x+4629995\)
32487.f3	32487l2	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{6} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.15	2Cs	$3.642679484$	$1$		$6$	$98304$	$1.434963$	$17806161424897/668584449$	$[1, 0, 0, -26657, -1622160]$	\(y^2+xy=x^3-26657x-1622160\)
32487.f4	32487l1	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$7.285358969$	$1$		$1$	$49152$	$1.088390$	$17319700013617/25857$	$[1, 0, 0, -26412, -1654353]$	\(y^2+xy=x^3-26412x-1654353\)
32487.f5	32487l3	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 7^{6} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.92	2B	$7.285358969$	$1$		$2$	$196608$	$1.781538$	$1193377118543/124806800313$	$[1, 0, 0, 10828, -5812983]$	\(y^2+xy=x^3+10828x-5812983\)
32487.f6	32487l5	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{4} \cdot 7^{6} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.91	2B	$3.642679484$	$1$		$2$	$393216$	$2.128113$	$6439735268725823/7345472585373$	$[1, 0, 0, 189923, 31408838]$	\(y^2+xy=x^3+189923x+31408838\)
32487.g1	32487e1	32487.g	32487e	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 7^{3} \cdot 13 \cdot 17^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.210309761$	$1$		$6$	$20992$	$0.595311$	$-239251750912/9771957$	$[0, -1, 1, -905, 11150]$	\(y^2+y=x^3-x^2-905x+11150\)
32487.h1	32487q1	32487.h	32487q	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 7^{9} \cdot 13 \cdot 17^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$146944$	$1.568266$	$-239251750912/9771957$	$[0, 1, 1, -44361, -3735826]$	\(y^2+y=x^3+x^2-44361x-3735826\)
32487.i1	32487f1	32487.i	32487f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{3} \cdot 7^{7} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.497837884$	$1$		$1$	$36864$	$0.844235$	$10431681625/710073$	$[1, 1, 0, -2230, -39017]$	\(y^2+xy=x^3+x^2-2230x-39017\)
32487.i2	32487f2	32487.i	32487f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{6} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4.248918942$	$1$		$0$	$73728$	$1.190809$	$6804992375/102626433$	$[1, 1, 0, 1935, -163134]$	\(y^2+xy=x^3+x^2+1935x-163134\)
32487.j1	32487r2	32487.j	32487r	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 7^{6} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$207360$	$1.449699$	$3885442650361/1996623837$	$[1, 0, 1, -16049, 260579]$	\(y^2+xy+y=x^3-16049x+260579\)
32487.j2	32487r1	32487.j	32487r	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{6} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$103680$	$1.103127$	$2000852317801/2094417$	$[1, 0, 1, -12864, 559969]$	\(y^2+xy+y=x^3-12864x+559969\)
32487.k1	32487c1	32487.k	32487c	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{2} \cdot 13^{5} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$84480$	$1.041748$	$6441016595550208/511270461$	$[0, -1, 1, -14184, 654905]$	\(y^2+y=x^3-x^2-14184x+654905\)
32487.l1	32487h1	32487.l	32487h	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{10} \cdot 13^{3} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$592704$	$1.883810$	$776703004672/97144749$	$[0, -1, 1, -125652, -15136549]$	\(y^2+y=x^3-x^2-125652x-15136549\)
32487.m1	32487a1	32487.m	32487a	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{4} \cdot 13 \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2.755768110$	$1$		$0$	$16896$	$0.378708$	$15957372928/17901$	$[0, -1, 1, -702, 7391]$	\(y^2+y=x^3-x^2-702x+7391\)
32487.n1	32487d1	32487.n	32487d	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{6} \cdot 7^{7} \cdot 13 \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$198144$	$1.549738$	$-2731787761881088/19171971$	$[0, -1, 1, -142704, 20797013]$	\(y^2+y=x^3-x^2-142704x+20797013\)
32487.o1	32487j1	32487.o	32487j	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{4} \cdot 13^{3} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$84672$	$0.910855$	$776703004672/97144749$	$[0, 1, 1, -2564, 43397]$	\(y^2+y=x^3+x^2-2564x+43397\)
32487.p1	32487p1	32487.p	32487p	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{10} \cdot 13 \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$8.450689736$	$1$		$0$	$118272$	$1.351664$	$15957372928/17901$	$[0, 1, 1, -34414, -2466383]$	\(y^2+y=x^3+x^2-34414x-2466383\)
32487.q1	32487o1	32487.q	32487o	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{22} \cdot 7^{7} \cdot 13 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2.043068911$	$1$		$0$	$1571328$	$2.536655$	$-1302227927110660096/825290486657091$	$[0, 1, 1, -1114766, -656107273]$	\(y^2+y=x^3+x^2-1114766x-656107273\)
32487.r1	32487k1	32487.r	32487k	$1$	$1$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{8} \cdot 13^{5} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$591360$	$2.014702$	$6441016595550208/511270461$	$[0, 1, 1, -695032, -223242449]$	\(y^2+y=x^3+x^2-695032x-223242449\)