LMFDB - Elliptic curves over $\Q$ of conductor 4488

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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

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Results (23 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4488.a1	4488c1	4488.a	4488c	$1$	$1$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{8} \cdot 3^{4} \cdot 11 \cdot 17^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$374$	$2$	$0$	$0.105751671$	$1$	$12$	$3072$	$0.419039$	$1055028224/4377483$	$0.89121$	$3.34655$	$[0, -1, 0, 135, -1539]$	$y^2=x^3-x^2+135x-1539$	374.2.0.?	$[(45, 306)]$
4488.b1	4488a2	4488.b	4488a	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.806927060$	$1$	$3$	$2304$	$0.579484$	$30248395634/1499553$	$0.88414$	$3.77651$	$[0, -1, 0, -824, -8436]$	$y^2=x^3-x^2-824x-8436$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-15, 18)]$
4488.b2	4488a1	4488.b	4488a	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.403463530$	$1$	$5$	$1152$	$0.232911$	$324730948/85833$	$0.83181$	$3.15489$	$[0, -1, 0, -144, 540]$	$y^2=x^3-x^2-144x+540$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[(2, 16)]$
4488.c1	4488f3	4488.c	4488f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{3} \cdot 11 \cdot 17^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.102	2B	$264$	$48$	$0$	$4.323630485$	$1$	$1$	$24576$	$1.688204$	$3590504967602306/2071799959977$	$1.05249$	$5.16599$	$[0, -1, 0, -40512, 182700]$	$y^2=x^3-x^2-40512x+182700$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 132.12.0.?, 264.48.0.?	$[(3977/4, 148835/4)]$
4488.c2	4488f2	4488.c	4488f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3^{6} \cdot 11^{2} \cdot 17^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.4	2Cs	$264$	$48$	$0$	$2.161815242$	$1$	$7$	$12288$	$1.341631$	$2535093488117092/7367303889$	$1.01810$	$5.04218$	$[0, -1, 0, -28632, 1869660]$	$y^2=x^3-x^2-28632x+1869660$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 132.24.0.?, 264.48.0.?	$[(77, 340)]$
4488.c3	4488f1	4488.c	4488f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.53	2B	$264$	$48$	$0$	$4.323630485$	$1$	$5$	$6144$	$0.995057$	$10119139303540048/85833$	$0.96209$	$5.04193$	$[0, -1, 0, -28612, 1872388]$	$y^2=x^3-x^2-28612x+1872388$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 66.6.0.a.1, 132.24.0.?, $\ldots$	$[(-64, 1854)]$
4488.c4	4488f4	4488.c	4488f	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{11} \cdot 3^{12} \cdot 11^{4} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.59	2B	$264$	$48$	$0$	$4.323630485$	$1$	$3$	$24576$	$1.688204$	$-268702931670626/2248659199809$	$0.99347$	$5.18334$	$[0, -1, 0, -17072, 3381708]$	$y^2=x^3-x^2-17072x+3381708$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 264.48.0.?	$[(213, 3060)]$
4488.d1	4488b1	4488.d	4488b	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{3} \cdot 11 \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$1920$	$0.104249$	$192143824/85833$	$0.82047$	$2.92763$	$[0, -1, 0, -76, 148]$	$y^2=x^3-x^2-76x+148$	2.3.0.a.1, 66.6.0.a.1, 68.6.0.b.1, 2244.12.0.?	$[ ]$
4488.d2	4488b2	4488.d	4488b	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{6} \cdot 11^{2} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$3840$	$0.450823$	$1979654684/1499553$	$0.87760$	$3.36986$	$[0, -1, 0, 264, 828]$	$y^2=x^3-x^2+264x+828$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[ ]$
4488.e1	4488h2	4488.e	4488h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$11520$	$1.336094$	$110725946217794/21954955473$	$0.95362$	$4.75228$	$[0, 1, 0, -12704, -451104]$	$y^2=x^3+x^2-12704x-451104$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
4488.e2	4488h1	4488.e	4488h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3^{3} \cdot 11^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$	$1$	$5760$	$0.989520$	$187761599684068/10385793$	$0.94659$	$4.73266$	$[0, 1, 0, -12024, -511488]$	$y^2=x^3+x^2-12024x-511488$	2.3.0.a.1, 66.6.0.a.1, 136.6.0.?, 4488.12.0.?	$[ ]$
4488.f1	4488k1	4488.f	4488k	$1$	$1$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{8} \cdot 3^{6} \cdot 11^{3} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$374$	$2$	$0$	$0.094314145$	$1$	$10$	$2304$	$0.532147$	$-3962770432/16495083$	$0.90694$	$3.53765$	$[0, 1, 0, -209, 3267]$	$y^2=x^3+x^2-209x+3267$	374.2.0.?	$[(-11, 66)]$
4488.g1	4488g1	4488.g	4488g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3 \cdot 11 \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$4488$	$12$	$0$	$6.595417320$	$1$	$1$	$896$	$0.033397$	$676449508/561$	$0.83058$	$3.24216$	$[0, 1, 0, -184, -1024]$	$y^2=x^3+x^2-184x-1024$	2.3.0.a.1, 8.6.0.d.1, 1122.6.0.?, 4488.12.0.?	$[(601/4, 13797/4)]$
4488.g2	4488g2	4488.g	4488g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{11} \cdot 3^{2} \cdot 11^{2} \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$4488$	$12$	$0$	$3.297708660$	$1$	$3$	$1792$	$0.379971$	$-162365474/314721$	$0.85819$	$3.32971$	$[0, 1, 0, -144, -1440]$	$y^2=x^3+x^2-144x-1440$	2.3.0.a.1, 8.6.0.a.1, 2244.6.0.?, 4488.12.0.?	$[(147, 1782)]$
4488.h1	4488d1	4488.h	4488d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3 \cdot 11^{3} \cdot 17^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$1920$	$0.536475$	$967473250000/1153977$	$0.95116$	$3.94131$	$[0, 1, 0, -1308, 17760]$	$y^2=x^3+x^2-1308x+17760$	2.3.0.a.1, 66.6.0.a.1, 68.6.0.b.1, 2244.12.0.?	$[ ]$
4488.h2	4488d2	4488.h	4488d	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{2} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$1$	$1$	$1$	$3840$	$0.883048$	$-98061470500/271048833$	$0.92244$	$4.04251$	$[0, 1, 0, -968, 27552]$	$y^2=x^3+x^2-968x+27552$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[ ]$
4488.i1	4488j1	4488.i	4488j	$1$	$1$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{8} \cdot 3^{8} \cdot 11^{7} \cdot 17^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$374$	$2$	$0$	$0.114237895$	$1$	$10$	$107520$	$2.525993$	$-2737717077365028736000/181536283769982867$	$1.03399$	$6.54228$	$[0, 1, 0, -1850553, -1023572133]$	$y^2=x^3+x^2-1850553x-1023572133$	374.2.0.?	$[(3321, 171666)]$
4488.j1	4488i1	4488.j	4488i	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{5} \cdot 11 \cdot 17^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$0.242464564$	$1$	$11$	$1920$	$0.465278$	$282841522000/772497$	$0.95384$	$3.79507$	$[0, 1, 0, -868, 9536]$	$y^2=x^3+x^2-868x+9536$	2.3.0.a.1, 66.6.0.a.1, 68.6.0.b.1, 2244.12.0.?	$[(14, 18)]$
4488.j2	4488i2	4488.j	4488i	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{10} \cdot 3^{10} \cdot 11^{2} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2244$	$12$	$0$	$0.484929129$	$1$	$9$	$3840$	$0.811852$	$-15927506500/121463793$	$0.99730$	$3.93315$	$[0, 1, 0, -528, 17424]$	$y^2=x^3+x^2-528x+17424$	2.3.0.a.1, 68.6.0.a.1, 132.6.0.?, 2244.12.0.?	$[(0, 132)]$
4488.k1	4488e4	4488.k	4488e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3^{3} \cdot 11 \cdot 17^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4488$	$48$	$0$	$1$	$1$	$1$	$4608$	$0.922907$	$28742820444292/24805737$	$0.93411$	$4.50947$	$[0, 1, 0, -6432, 196272]$	$y^2=x^3+x^2-6432x+196272$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.1, 66.6.0.a.1, $\ldots$	$[ ]$
4488.k2	4488e3	4488.k	4488e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{10} \cdot 3^{12} \cdot 11 \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4488$	$48$	$0$	$1$	$1$	$1$	$4608$	$0.922907$	$8187726931492/99379467$	$0.92532$	$4.36014$	$[0, 1, 0, -4232, -106272]$	$y^2=x^3+x^2-4232x-106272$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 44.12.0-4.c.1.2, 68.12.0-4.c.1.1, $\ldots$	$[ ]$
4488.k3	4488e2	4488.k	4488e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{8} \cdot 3^{6} \cdot 11^{2} \cdot 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$2244$	$48$	$0$	$1$	$1$	$3$	$2304$	$0.576333$	$51553893328/25492401$	$0.90082$	$3.59264$	$[0, 1, 0, -492, 1440]$	$y^2=x^3+x^2-492x+1440$	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 68.12.0-2.a.1.1, 132.24.0.?, $\ldots$	$[ ]$
4488.k4	4488e1	4488.k	4488e	$4$	$4$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ - 2^{4} \cdot 3^{3} \cdot 11^{4} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$4488$	$48$	$0$	$1$	$1$	$1$	$1152$	$0.229760$	$9885304832/6720219$	$1.04813$	$3.06652$	$[0, 1, 0, 113, 230]$	$y^2=x^3+x^2+113x+230$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 68.12.0-4.c.1.2, 88.12.0.?, $\ldots$	$[ ]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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