LMFDB - Elliptic curves over $\Q$ of conductor 9522

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

Intrinsic torsion order

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Results (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
9522.a1	9522b1	9522.a	9522b	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{5} \cdot 3^{9} \cdot 23^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$1$	$1$		$0$	$66240$	$1.882809$	$621/32$	$1.16643$	$5.00806$	$1$	$[1, -1, 0, 20532, 10620080]$	$y^2+xy=x^3-x^2+20532x+10620080$	24.2.0.b.1	$[ ]$	$1$
9522.b1	9522d1	9522.b	9522d	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{14} \cdot 3^{10} \cdot 23^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$276$	$16$	$0$	$1.965002818$	$1$		$2$	$10752$	$0.944289$	$-1550640289/1327104$	$1.00450$	$3.81302$	$1$	$[1, -1, 0, -1755, -44123]$	$y^2+xy=x^3-x^2-1755x-44123$	4.8.0.b.1, 276.16.0.?	$[(54, 101)]$	$1$
9522.c1	9522c1	9522.c	9522c	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{14} \cdot 3^{10} \cdot 23^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$12$	$16$	$0$	$4.728795649$	$1$		$2$	$247296$	$2.512035$	$-1550640289/1327104$	$1.00450$	$5.86653$	$1$	$[1, -1, 0, -928494, 542415316]$	$y^2+xy=x^3-x^2-928494x+542415316$	4.8.0.b.1, 12.16.0-4.b.1.1	$[(-84, 24938)]$	$1$
9522.d1	9522e4	9522.d	9522e	$4$	$4$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2 \cdot 3^{14} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$552$	$48$	$0$	$2.673270847$	$1$		$0$	$135168$	$2.172066$	$1666957239793/301806$	$1.06466$	$5.84484$	$2$	$[1, -1, 0, -1176066, 491120302]$	$y^2+xy=x^3-x^2-1176066x+491120302$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.1, 24.24.0-8.p.1.3, $\ldots$	$[(2439/2, 2851/2)]$	$1$
9522.d2	9522e3	9522.d	9522e	$4$	$4$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2 \cdot 3^{8} \cdot 23^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.15	2B	$552$	$48$	$0$	$10.69308339$	$1$		$0$	$135168$	$2.172066$	$135559106353/5037138$	$0.97631$	$5.57093$	$2$	$[1, -1, 0, -509526, -135293990]$	$y^2+xy=x^3-x^2-509526x-135293990$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 24.24.0-8.k.1.3, 184.24.0.?, $\ldots$	$[(91259/10, 12157853/10)]$	$1$
9522.d3	9522e2	9522.d	9522e	$4$	$4$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2^{2} \cdot 3^{10} \cdot 23^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.3	2Cs	$552$	$48$	$0$	$5.346541695$	$1$		$2$	$67584$	$1.825495$	$545338513/171396$	$0.94447$	$4.96886$	$1$	$[1, -1, 0, -81036, 6022012]$	$y^2+xy=x^3-x^2-81036x+6022012$	2.6.0.a.1, 8.12.0.a.1, 12.12.0-2.a.1.1, 24.24.0-8.a.1.3, 92.12.0.?, $\ldots$	$[(1619/2, 48601/2)]$	$1$
9522.d4	9522e1	9522.d	9522e	$4$	$4$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{4} \cdot 3^{8} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$552$	$48$	$0$	$2.673270847$	$1$		$3$	$33792$	$1.478920$	$2924207/3312$	$0.89878$	$4.39816$	$2$	$[1, -1, 0, 14184, 632560]$	$y^2+xy=x^3-x^2+14184x+632560$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.2, 24.24.0-8.p.1.1, $\ldots$	$[(8, 860)]$	$1$
9522.e1	9522a1	9522.e	9522a	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{5} \cdot 3^{9} \cdot 23^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$1$	$1$		$0$	$2880$	$0.315063$	$621/32$	$1.16643$	$2.95455$	$1$	$[1, -1, 0, 39, -883]$	$y^2+xy=x^3-x^2+39x-883$	24.2.0.b.1	$[ ]$	$1$
9522.f1	9522o2	9522.f	9522o	$2$	$3$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{6} \cdot 3^{6} \cdot 23^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.8.0.1	3B.1.1	$12$	$32$	$0$	$1$	$1$		$2$	$132480$	$1.983732$	$-313994137/64$	$0.96923$	$5.59315$	$1$	$[1, -1, 1, -545234, 155124497]$	$y^2+xy+y=x^3-x^2-545234x+155124497$	3.8.0-3.a.1.2, 4.2.0.a.1, 12.32.0-12.b.2.3	$[ ]$	$1$
9522.f2	9522o1	9522.f	9522o	$2$	$3$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{2} \cdot 3^{6} \cdot 23^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.8.0.2	3B.1.2	$12$	$32$	$0$	$1$	$1$		$0$	$44160$	$1.434427$	$23/4$	$0.94596$	$4.42219$	$1$	$[1, -1, 1, 2281, 725267]$	$y^2+xy+y=x^3-x^2+2281x+725267$	3.8.0-3.a.1.1, 4.2.0.a.1, 12.32.0-12.b.1.3	$[ ]$	$1$
9522.g1	9522l1	9522.g	9522l	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 23^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$270480$	$2.473545$	$-97967097/128$	$1.09650$	$6.15073$	$1$	$[1, -1, 1, -2990801, 1993801537]$	$y^2+xy+y=x^3-x^2-2990801x+1993801537$	8.2.0.a.1	$[ ]$	$1$
9522.h1	9522g1	9522.h	9522g	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{5} \cdot 3^{3} \cdot 23^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$0.265456975$	$1$		$6$	$960$	$-0.234244$	$621/32$	$1.16643$	$2.23504$	$1$	$[1, -1, 1, 4, 31]$	$y^2+xy+y=x^3-x^2+4x+31$	24.2.0.b.1	$[(1, 5)]$	$1$
9522.i1	9522k2	9522.i	9522k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2 \cdot 3^{7} \cdot 23^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$0$	$67584$	$1.712502$	$3463512697/3174$	$0.94552$	$5.17065$	$1$	$[1, -1, 1, -150071, 22396281]$	$y^2+xy+y=x^3-x^2-150071x+22396281$	2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.?	$[ ]$	$1$
9522.i2	9522k1	9522.i	9522k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{2} \cdot 3^{8} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$1$	$33792$	$1.365929$	$-389017/828$	$0.87759$	$4.34639$	$1$	$[1, -1, 1, -7241, 514725]$	$y^2+xy+y=x^3-x^2-7241x+514725$	2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.?	$[ ]$	$1$
9522.j1	9522m1	9522.j	9522m	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{7} \cdot 3^{13} \cdot 23^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$1$	$1$		$0$	$18816$	$0.923532$	$-20285403817/279936$	$1.00360$	$3.99716$	$1$	$[1, -1, 1, -4136, -102549]$	$y^2+xy+y=x^3-x^2-4136x-102549$	24.2.0.b.1	$[ ]$	$1$
9522.k1	9522h4	9522.k	9522h	$4$	$6$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2^{6} \cdot 3^{7} \cdot 23^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$276$	$96$	$1$	$1$	$1$		$0$	$405504$	$2.813065$	$50591419971625/28422890688$	$1.07125$	$6.21736$	$1$	$[1, -1, 1, -3668450, 462951713]$	$y^2+xy+y=x^3-x^2-3668450x+462951713$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.h.1.2, 69.8.0-3.a.1.2, $\ldots$	$[ ]$	$1$
9522.k2	9522h2	9522.k	9522h	$4$	$6$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2^{2} \cdot 3^{9} \cdot 23^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$276$	$96$	$1$	$1$	$1$		$0$	$135168$	$2.263756$	$21081759765625/57132$	$1.12484$	$6.12181$	$1$	$[1, -1, 1, -2740055, 1746450659]$	$y^2+xy+y=x^3-x^2-2740055x+1746450659$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.h.1.4, 69.8.0-3.a.1.1, $\ldots$	$[ ]$	$1$
9522.k3	9522h1	9522.k	9522h	$4$	$6$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{4} \cdot 3^{12} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$276$	$96$	$1$	$1$	$1$		$1$	$67584$	$1.917183$	$-4956477625/268272$	$0.95072$	$5.21953$	$1$	$[1, -1, 1, -169115, 28034363]$	$y^2+xy+y=x^3-x^2-169115x+28034363$	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 12.48.0-12.i.1.3, 46.6.0.a.1, $\ldots$	$[ ]$	$1$
9522.k4	9522h3	9522.k	9522h	$4$	$6$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{12} \cdot 3^{8} \cdot 23^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$276$	$96$	$1$	$1$	$1$		$1$	$202752$	$2.466488$	$752329532375/448524288$	$1.05431$	$5.75800$	$1$	$[1, -1, 1, 902110, 57085985]$	$y^2+xy+y=x^3-x^2+902110x+57085985$	2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 12.48.0-12.i.1.1, 46.6.0.a.1, $\ldots$	$[ ]$	$1$
9522.l1	9522j1	9522.l	9522j	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{7} \cdot 3^{13} \cdot 23^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$1$	$1$		$0$	$432768$	$2.491280$	$-20285403817/279936$	$1.00360$	$6.05067$	$1$	$[1, -1, 1, -2187779, 1260837123]$	$y^2+xy+y=x^3-x^2-2187779x+1260837123$	24.2.0.b.1	$[ ]$	$1$
9522.m1	9522f1	9522.m	9522f	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{5} \cdot 3^{3} \cdot 23^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$24$	$2$	$0$	$0.810144449$	$1$		$2$	$22080$	$1.333504$	$621/32$	$1.16643$	$4.28855$	$1$	$[1, -1, 1, 2281, -394097]$	$y^2+xy+y=x^3-x^2+2281x-394097$	24.2.0.b.1	$[(397, 7736)]$	$1$
9522.n1	9522i1	9522.n	9522i	$1$	$1$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 23^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$11760$	$0.905796$	$-97967097/128$	$1.09650$	$4.09721$	$1$	$[1, -1, 1, -5654, -162395]$	$y^2+xy+y=x^3-x^2-5654x-162395$	8.2.0.a.1	$[ ]$	$1$
9522.o1	9522n2	9522.o	9522n	$2$	$3$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{6} \cdot 3^{6} \cdot 23^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.4.0.1	3B	$276$	$32$	$0$	$1$	$1$		$0$	$5760$	$0.415986$	$-313994137/64$	$0.96923$	$3.53964$	$1$	$[1, -1, 1, -1031, -12481]$	$y^2+xy+y=x^3-x^2-1031x-12481$	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.2, 69.8.0-3.a.1.2, 276.32.0.?	$[ ]$	$1$
9522.o2	9522n1	9522.o	9522n	$2$	$3$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{2} \cdot 3^{6} \cdot 23^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.4.0.1	3B	$276$	$32$	$0$	$1$	$1$		$0$	$1920$	$-0.133320$	$23/4$	$0.94596$	$2.36868$	$1$	$[1, -1, 1, 4, -61]$	$y^2+xy+y=x^3-x^2+4x-61$	3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.1, 69.8.0-3.a.1.1, 276.32.0.?	$[ ]$	$1$
9522.p1	9522p2	9522.p	9522p	$2$	$2$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ 2^{5} \cdot 3^{6} \cdot 23^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$184$	$12$	$0$	$1$	$4$	$2$	$0$	$168960$	$2.025146$	$545138290809/16928$	$1.08081$	$5.72283$	$1$	$[1, -1, 1, -810263, -280518641]$	$y^2+xy+y=x^3-x^2-810263x-280518641$	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?	$[ ]$	$1$
9522.p2	9522p1	9522.p	9522p	$2$	$2$	$ 2 \cdot 3^{2} \cdot 23^{2} $	$ - 2^{10} \cdot 3^{6} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$184$	$12$	$0$	$1$	$1$		$1$	$84480$	$1.678572$	$-116930169/23552$	$1.03422$	$4.83339$	$1$	$[1, -1, 1, -48503, -4761521]$	$y^2+xy+y=x^3-x^2-48503x-4761521$	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?	$[ ]$	$1$

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