Elliptic curves over $\Q$ of conductor 267589

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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	Manin constant
267589.a1	267589a1	267589.a	267589a	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( 7^{6} \cdot 43 \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10922$	$2$	$0$	$1$	$1$		$0$	$140616$	$0.503534$	$481890304/5461$	$0.78193$	$2.53406$	$[0, 1, 1, -800, 8362]$	\(y^2+y=x^3+x^2-800x+8362\)	10922.2.0.?	$[ ]$	$1$
267589.b1	267589b1	267589.b	267589b	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( 7^{6} \cdot 43^{5} \cdot 127 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10922$	$2$	$0$	$14.35918341$	$1$		$0$	$1577400$	$1.930933$	$74631223079501824/18670072261$	$0.93189$	$4.04305$	$[0, 1, 1, -429795, 108286063]$	\(y^2+y=x^3+x^2-429795x+108286063\)	10922.2.0.?	$[(3205213/98, 1373372223/98)]$	$1$
267589.c1	267589c2	267589.c	267589c	$2$	$3$	\( 7^{2} \cdot 43 \cdot 127 \)	\( - 7^{7} \cdot 43 \cdot 127^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$229362$	$16$	$0$	$1$	$1$		$0$	$2799360$	$2.049305$	$-3114182784544768000/616563283$	$0.90872$	$4.34161$	$[0, -1, 1, -1490743, 701068472]$	\(y^2+y=x^3-x^2-1490743x+701068472\)	3.4.0.a.1, 21.8.0-3.a.1.2, 32766.8.0.?, 76454.2.0.?, 229362.16.0.?	$[ ]$	$1$
267589.c2	267589c1	267589.c	267589c	$2$	$3$	\( 7^{2} \cdot 43 \cdot 127 \)	\( - 7^{9} \cdot 43^{3} \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$229362$	$16$	$0$	$1$	$1$		$0$	$933120$	$1.500000$	$-3738308608000/3463404427$	$0.81994$	$3.32722$	$[0, -1, 1, -15843, 1243171]$	\(y^2+y=x^3-x^2-15843x+1243171\)	3.4.0.a.1, 21.8.0-3.a.1.1, 32766.8.0.?, 76454.2.0.?, 229362.16.0.?	$[ ]$	$1$
267589.d1	267589d1	267589.d	267589d	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( - 7^{9} \cdot 43 \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$76454$	$2$	$0$	$1$	$1$		$0$	$656640$	$1.071524$	$-1104224813056/1873123$	$0.78823$	$3.15339$	$[0, -1, 1, -10551, 421294]$	\(y^2+y=x^3-x^2-10551x+421294\)	76454.2.0.?	$[ ]$	$1$
267589.e1	267589e1	267589.e	267589e	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( 7^{3} \cdot 43^{3} \cdot 127 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152908$	$2$	$0$	$0.471544265$	$1$		$4$	$249984$	$0.662361$	$1404551713599/10097389$	$0.81494$	$2.70528$	$[1, -1, 0, -1633, 25654]$	\(y^2+xy=x^3-x^2-1633x+25654\)	152908.2.0.?	$[(18, 34)]$	$1$
267589.f1	267589f1	267589.f	267589f	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( - 7^{15} \cdot 43 \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$76454$	$2$	$0$	$1$	$1$		$0$	$2218752$	$1.835333$	$166220772680087/220371047827$	$0.84445$	$3.57481$	$[1, 0, 1, 56128, 5820021]$	\(y^2+xy+y=x^3+56128x+5820021\)	76454.2.0.?	$[ ]$	$1$
267589.g1	267589g1	267589.g	267589g	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( 7^{9} \cdot 43^{3} \cdot 127 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152908$	$2$	$0$	$12.23502249$	$1$		$0$	$1749888$	$1.635317$	$1404551713599/10097389$	$0.81494$	$3.63953$	$[1, -1, 0, -80026, -8639275]$	\(y^2+xy=x^3-x^2-80026x-8639275\)	152908.2.0.?	$[(31249108/309, 6421355345/309)]$	$1$
267589.h1	267589h1	267589.h	267589h	$1$	$1$	\( 7^{2} \cdot 43 \cdot 127 \)	\( - 7^{9} \cdot 43 \cdot 127 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$76454$	$2$	$0$	$1$	$1$		$0$	$352512$	$0.855484$	$512000/1873123$	$0.77728$	$2.68645$	$[0, 1, 1, 82, -22557]$	\(y^2+y=x^3+x^2+82x-22557\)	76454.2.0.?	$[ ]$	$1$

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