Elliptic curves over $\Q$ of conductor 17457

Results (12 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
17457.a1	17457b2	17457.a	17457b	$2$	$2$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{5} \cdot 11^{4} \cdot 23^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$0$	$168960$	$2.170235$	$209849322390625/1882056627$	$0.99362$	$5.30232$	$[1, 1, 1, -654913, 202137092]$	\(y^2+xy+y=x^3+x^2-654913x+202137092\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[]$
17457.a2	17457b1	17457.a	17457b	$2$	$2$	\( 3 \cdot 11 \cdot 23^{2} \)	\( - 3^{10} \cdot 11^{2} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$84480$	$1.823660$	$-1349232625/164333367$	$0.95842$	$4.62655$	$[1, 1, 1, -12178, 7516934]$	\(y^2+xy+y=x^3+x^2-12178x+7516934\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[]$
17457.b1	17457c5	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3 \cdot 11 \cdot 23^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$12144$	$192$	$1$	$26.17974545$	$1$		$0$	$540672$	$2.682854$	$89254274298475942657/17457$	$1.00726$	$6.62923$	$[1, 0, 0, -49252027, 133036520888]$	\(y^2+xy=x^3-49252027x+133036520888\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.7, $\ldots$	$[(2459205891403/24154, 225926560116674899/24154)]$
17457.b2	17457c4	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{2} \cdot 11^{2} \cdot 23^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$6072$	$192$	$1$	$13.08987272$	$1$		$2$	$270336$	$2.336281$	$21790813729717297/304746849$	$0.97272$	$5.77766$	$[1, 0, 0, -3078262, 2078488595]$	\(y^2+xy=x^3-3078262x+2078488595\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.h.1.3, 88.48.0.?, $\ldots$	$[(1219547/26, 844743619/26)]$
17457.b3	17457c6	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( - 3 \cdot 11 \cdot 23^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$12144$	$192$	$1$	$26.17974545$	$1$		$0$	$540672$	$2.682854$	$-19989223566735457/2584262514273$	$0.97497$	$5.78946$	$[1, 0, 0, -2990977, 2201927042]$	\(y^2+xy=x^3-2990977x+2201927042\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0.by.1, $\ldots$	$[(215553181819/10998, 65754056285562709/10998)]$
17457.b4	17457c3	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{2} \cdot 11^{8} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.56	2B	$12144$	$192$	$1$	$13.08987272$	$1$		$0$	$270336$	$2.336281$	$309368403125137/44372288367$	$0.95365$	$5.34206$	$[1, 0, 0, -745372, -214875583]$	\(y^2+xy=x^3-745372x-214875583\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 24.48.0-24.by.2.6, 92.24.0.?, $\ldots$	$[(644501/20, 414435541/20)]$
17457.b5	17457c2	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{4} \cdot 11^{4} \cdot 23^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$6072$	$192$	$1$	$6.544936362$	$1$		$4$	$135168$	$1.989708$	$5786435182177/627352209$	$0.98731$	$4.93468$	$[1, 0, 0, -197857, 30520640]$	\(y^2+xy=x^3-197857x+30520640\)	2.6.0.a.1, 4.24.0-4.b.1.2, 24.48.0-24.h.2.32, 88.48.0.?, 92.48.0.?, $\ldots$	$[(1520, 56180)]$
17457.b6	17457c1	17457.b	17457c	$6$	$8$	\( 3 \cdot 11 \cdot 23^{2} \)	\( - 3^{8} \cdot 11^{2} \cdot 23^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$12144$	$192$	$1$	$3.272468181$	$1$		$7$	$67584$	$1.643133$	$3288008303/18259263$	$0.97810$	$4.38985$	$[1, 0, 0, 16388, 2368847]$	\(y^2+xy=x^3+16388x+2368847\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 46.6.0.a.1, 48.48.0-48.f.2.18, $\ldots$	$[(-67, 1019)]$
17457.c1	17457a3	17457.c	17457a	$4$	$4$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{3} \cdot 11^{4} \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6072$	$48$	$0$	$1$	$1$		$0$	$67584$	$1.555115$	$347873904937/395307$	$1.00913$	$4.64685$	$[1, 1, 0, -77509, -8329922]$	\(y^2+xy=x^3+x^2-77509x-8329922\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 88.12.0.?, 92.12.0.?, $\ldots$	$[]$
17457.c2	17457a2	17457.c	17457a	$4$	$4$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{6} \cdot 11^{2} \cdot 23^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3036$	$48$	$0$	$1$	$1$		$2$	$33792$	$1.208542$	$169112377/88209$	$1.00669$	$3.86578$	$[1, 1, 0, -6094, -60065]$	\(y^2+xy=x^3+x^2-6094x-60065\)	2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 92.12.0.?, 132.24.0.?, $\ldots$	$[]$
17457.c3	17457a1	17457.c	17457a	$4$	$4$	\( 3 \cdot 11 \cdot 23^{2} \)	\( 3^{3} \cdot 11 \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6072$	$48$	$0$	$1$	$1$		$1$	$16896$	$0.861968$	$30664297/297$	$1.09706$	$3.69097$	$[1, 1, 0, -3449, 75888]$	\(y^2+xy=x^3+x^2-3449x+75888\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 66.6.0.a.1, 88.12.0.?, $\ldots$	$[]$
17457.c4	17457a4	17457.c	17457a	$4$	$4$	\( 3 \cdot 11 \cdot 23^{2} \)	\( - 3^{12} \cdot 11 \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6072$	$48$	$0$	$1$	$1$		$0$	$67584$	$1.555115$	$9090072503/5845851$	$1.03763$	$4.27371$	$[1, 1, 0, 23001, -438300]$	\(y^2+xy=x^3+x^2+23001x-438300\)	2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 44.12.0.g.1, $\ldots$	$[]$