Elliptic curves over $\Q$ of conductor 912

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 (28 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
912.a1	912a1	912.a	912a	$1$	$1$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{8} \cdot 3^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.134807958$	$1$		$2$	$192$	$-0.016677$	$-81415168/13851$	$[0, -1, 0, -57, -171]$	\(y^2=x^3-x^2-57x-171\)
912.b1	912g3	912.b	912g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{12} \cdot 3^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$2.601893913$	$1$		$3$	$384$	$0.448139$	$115714886617/1539$	$[0, -1, 0, -1624, -24656]$	\(y^2=x^3-x^2-1624x-24656\)
912.b2	912g2	912.b	912g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{12} \cdot 3^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1.300946956$	$1$		$9$	$192$	$0.101565$	$30664297/3249$	$[0, -1, 0, -104, -336]$	\(y^2=x^3-x^2-104x-336\)
912.b3	912g1	912.b	912g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{12} \cdot 3 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$0.650473478$	$1$		$7$	$96$	$-0.245009$	$389017/57$	$[0, -1, 0, -24, 48]$	\(y^2=x^3-x^2-24x+48\)
912.b4	912g4	912.b	912g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{12} \cdot 3 \cdot 19^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$2.601893913$	$1$		$7$	$384$	$0.448139$	$67419143/390963$	$[0, -1, 0, 136, -1872]$	\(y^2=x^3-x^2+136x-1872\)
912.c1	912e3	912.c	912e	$4$	$6$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{14} \cdot 3 \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$864$	$0.798649$	$8671983378625/82308$	$[0, -1, 0, -6848, 220416]$	\(y^2=x^3-x^2-6848x+220416\)
912.c2	912e4	912.c	912e	$4$	$6$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{13} \cdot 3^{2} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$1728$	$1.145224$	$-8078253774625/846825858$	$[0, -1, 0, -6688, 231040]$	\(y^2=x^3-x^2-6688x+231040\)
912.c3	912e1	912.c	912e	$4$	$6$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{18} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$288$	$0.249343$	$57066625/32832$	$[0, -1, 0, -128, 0]$	\(y^2=x^3-x^2-128x\)
912.c4	912e2	912.c	912e	$4$	$6$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{15} \cdot 3^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$576$	$0.595917$	$3616805375/2105352$	$[0, -1, 0, 512, -512]$	\(y^2=x^3-x^2+512x-512\)
912.d1	912f2	912.d	912f	$2$	$5$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{12} \cdot 3^{2} \cdot 19^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$0.226284916$	$1$		$4$	$2400$	$1.344555$	$-9358714467168256/22284891$	$[0, -1, 0, -70245, 7189389]$	\(y^2=x^3-x^2-70245x+7189389\)
912.d2	912f1	912.d	912f	$2$	$5$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{12} \cdot 3^{10} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$1.131424581$	$1$		$2$	$480$	$0.539836$	$841232384/1121931$	$[0, -1, 0, 315, 2349]$	\(y^2=x^3-x^2+315x+2349\)
912.e1	912b3	912.e	912b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{11} \cdot 3^{3} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1$	$1$		$1$	$384$	$0.666203$	$111223479026/3518667$	$[0, -1, 0, -1272, -16560]$	\(y^2=x^3-x^2-1272x-16560\)
912.e2	912b2	912.e	912b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{10} \cdot 3^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$192$	$0.319629$	$768400132/263169$	$[0, -1, 0, -192, 720]$	\(y^2=x^3-x^2-192x+720\)
912.e3	912b1	912.e	912b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{8} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$1$		$1$	$96$	$-0.026945$	$2211014608/513$	$[0, -1, 0, -172, 928]$	\(y^2=x^3-x^2-172x+928\)
912.e4	912b4	912.e	912b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{11} \cdot 3^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1$	$1$		$1$	$384$	$0.666203$	$9878111854/10097379$	$[0, -1, 0, 568, 4368]$	\(y^2=x^3-x^2+568x+4368\)
912.f1	912i1	912.f	912i	$1$	$1$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{8} \cdot 3^{2} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.344049278$	$1$		$6$	$96$	$-0.429106$	$8192/171$	$[0, 1, 0, 3, -9]$	\(y^2=x^3+x^2+3x-9\)
912.g1	912l1	912.g	912l	$1$	$1$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{12} \cdot 3^{2} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$160$	$-0.143401$	$-1404928/171$	$[0, 1, 0, -37, -109]$	\(y^2=x^3+x^2-37x-109\)
912.h1	912h1	912.h	912h	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{14} \cdot 3^{5} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$0.269535280$	$1$		$11$	$480$	$0.512457$	$96386901625/18468$	$[0, 1, 0, -1528, 22484]$	\(y^2=x^3+x^2-1528x+22484\)
912.h2	912h2	912.h	912h	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{13} \cdot 3^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$0.134767640$	$1$		$15$	$960$	$0.859030$	$-69173457625/42633378$	$[0, 1, 0, -1368, 27540]$	\(y^2=x^3+x^2-1368x+27540\)
912.i1	912c1	912.i	912c	$1$	$1$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{8} \cdot 3^{2} \cdot 19^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$192$	$0.068805$	$70575104/61731$	$[0, 1, 0, 55, -93]$	\(y^2=x^3+x^2+55x-93\)
912.j1	912j2	912.j	912j	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$144$	$0.022556$	$340062928/13851$	$[0, 1, 0, -92, -360]$	\(y^2=x^3+x^2-92x-360\)
912.j2	912j1	912.j	912j	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$72$	$-0.324018$	$131072/9747$	$[0, 1, 0, 3, -18]$	\(y^2=x^3+x^2+3x-18\)
912.k1	912k3	912.k	912k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{17} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.104	2B	$1$	$1$		$1$	$5760$	$1.794586$	$74220219816682217473/16416$	$[0, 1, 0, -1400832, 637689780]$	\(y^2=x^3+x^2-1400832x+637689780\)
912.k2	912k2	912.k	912k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{22} \cdot 3^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.3	2Cs	$1$	$1$		$3$	$2880$	$1.448013$	$18120364883707393/269485056$	$[0, 1, 0, -87552, 9941940]$	\(y^2=x^3+x^2-87552x+9941940\)
912.k3	912k4	912.k	912k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{17} \cdot 3^{12} \cdot 19^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.48	2B	$1$	$1$		$3$	$5760$	$1.794586$	$-16576888679672833/2216253521952$	$[0, 1, 0, -84992, 10553268]$	\(y^2=x^3+x^2-84992x+10553268\)
912.k4	912k1	912.k	912k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{32} \cdot 3^{3} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.63	2B	$1$	$1$		$1$	$1440$	$1.101439$	$4824238966273/537919488$	$[0, 1, 0, -5632, 144308]$	\(y^2=x^3+x^2-5632x+144308\)
912.l1	912d1	912.l	912d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1$	$1$		$1$	$160$	$-0.354923$	$470596/57$	$[0, 1, 0, -16, -28]$	\(y^2=x^3+x^2-16x-28\)
912.l2	912d2	912.l	912d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 19 \)	\( - 2^{11} \cdot 3^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$1$	$1$		$1$	$320$	$-0.008349$	$715822/3249$	$[0, 1, 0, 24, -108]$	\(y^2=x^3+x^2+24x-108\)