Elliptic curves over $\Q$ of conductor 40344

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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
40344.a1	40344c1	40344.a	40344c	$1$	$1$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 41^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$246$	$2$	$0$	$1$	$1$		$0$	$161280$	$1.584324$	$128000/1107$	$0.84243$	$3.98121$	$[0, -1, 0, 11207, 1701421]$	\(y^2=x^3-x^2+11207x+1701421\)	246.2.0.?	$[ ]$
40344.b1	40344d2	40344.b	40344d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{11} \cdot 3^{4} \cdot 41^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.2	2B	$328$	$12$	$0$	$1$	$4$	$2$	$1$	$33280$	$0.730572$	$5142706/81$	$0.92628$	$3.22657$	$[0, -1, 0, -1872, -30132]$	\(y^2=x^3-x^2-1872x-30132\)	2.3.0.a.1, 8.6.0.f.1, 164.6.0.?, 328.12.0.?	$[ ]$
40344.b2	40344d1	40344.b	40344d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 41^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.2	2B	$328$	$12$	$0$	$1$	$1$		$1$	$16640$	$0.383998$	$19652/9$	$0.85441$	$2.63627$	$[0, -1, 0, -232, 700]$	\(y^2=x^3-x^2-232x+700\)	2.3.0.a.1, 8.6.0.f.1, 82.6.0.?, 328.12.0.?	$[ ]$
40344.c1	40344g6	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{11} \cdot 3^{2} \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.210	2B	$1968$	$192$	$1$	$16.32971129$	$1$		$1$	$276480$	$1.904581$	$3065617154/9$	$1.21059$	$4.87964$	$[0, 1, 0, -646064, -200091360]$	\(y^2=x^3+x^2-646064x-200091360\)	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, $\ldots$	$[(-140103065/549, 2531178980/549)]$
40344.c2	40344g4	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{10} \cdot 3 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.127	2B	$1968$	$192$	$1$	$8.164855646$	$1$		$3$	$138240$	$1.558008$	$28756228/3$	$1.05617$	$4.37401$	$[0, 1, 0, -108144, 13651152]$	\(y^2=x^3+x^2-108144x+13651152\)	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, $\ldots$	$[(9992, 998316)]$
40344.c3	40344g3	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 41^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.88	2Cs	$984$	$192$	$1$	$8.164855646$	$1$		$3$	$138240$	$1.558008$	$1556068/81$	$1.03212$	$4.09899$	$[0, 1, 0, -40904, -3051264]$	\(y^2=x^3+x^2-40904x-3051264\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 164.24.0.?, $\ldots$	$[(-10976/9, 107360/9)]$
40344.c4	40344g2	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 41^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.138	2Cs	$984$	$192$	$1$	$4.082427823$	$1$		$7$	$69120$	$1.211433$	$35152/9$	$0.97255$	$3.61088$	$[0, 1, 0, -7284, 176256]$	\(y^2=x^3+x^2-7284x+176256\)	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, $\ldots$	$[(-94, 198)]$
40344.c5	40344g1	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{4} \cdot 3 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.150	2B	$1968$	$192$	$1$	$8.164855646$	$1$		$1$	$34560$	$0.864861$	$2048/3$	$1.17572$	$3.12156$	$[0, 1, 0, 1121, 18242]$	\(y^2=x^3+x^2+1121x+18242\)	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, $\ldots$	$[(-1613/11, 44289/11)]$
40344.c6	40344g5	40344.c	40344g	$6$	$8$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{11} \cdot 3^{8} \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.218	2B	$1968$	$192$	$1$	$4.082427823$	$1$		$1$	$276480$	$1.904581$	$207646/6561$	$1.15980$	$4.34987$	$[0, 1, 0, 26336, -12034528]$	\(y^2=x^3+x^2+26336x-12034528\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 164.12.0.?, $\ldots$	$[(1789/2, 75645/2)]$
40344.d1	40344f1	40344.d	40344f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{8} \cdot 3^{5} \cdot 41^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$246$	$2$	$0$	$1.483147672$	$1$		$4$	$806400$	$2.403885$	$-21764027392/16747803$	$0.95864$	$4.94813$	$[0, 1, 0, -620849, 287188515]$	\(y^2=x^3+x^2-620849x+287188515\)	246.2.0.?	$[(1093, 30258)]$
40344.e1	40344a1	40344.e	40344a	$1$	$1$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{11} \cdot 3^{9} \cdot 41^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$984$	$2$	$0$	$1$	$1$		$0$	$725760$	$2.309517$	$334568302/807003$	$0.93145$	$4.77950$	$[0, 1, 0, 308744, 117631088]$	\(y^2=x^3+x^2+308744x+117631088\)	984.2.0.?	$[ ]$
40344.f1	40344b1	40344.f	40344b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 41^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$246$	$2$	$0$	$1$	$1$		$0$	$483840$	$2.046352$	$-83131122688/1107$	$0.95090$	$4.99475$	$[0, 1, 0, -970497, -368320797]$	\(y^2=x^3+x^2-970497x-368320797\)	246.2.0.?	$[ ]$
40344.g1	40344e2	40344.g	40344e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{11} \cdot 3^{4} \cdot 41^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.2	2B	$328$	$12$	$0$	$36.05523472$	$1$		$1$	$1364480$	$2.587357$	$5142706/81$	$0.92628$	$5.32756$	$[0, 1, 0, -3147392, -2120788512]$	\(y^2=x^3+x^2-3147392x-2120788512\)	2.3.0.a.1, 8.6.0.f.1, 164.6.0.?, 328.12.0.?	$[(-18952100141932769/4177567, 306325699800779309662440/4177567)]$
40344.g2	40344e1	40344.g	40344e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 41^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 41^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.2	2B	$328$	$12$	$0$	$18.02761736$	$1$		$1$	$682240$	$2.240784$	$19652/9$	$0.85441$	$4.73726$	$[0, 1, 0, -390552, 42779520]$	\(y^2=x^3+x^2-390552x+42779520\)	2.3.0.a.1, 8.6.0.f.1, 82.6.0.?, 328.12.0.?	$[(50176488/739, 1118474541120/739)]$

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