LMFDB - Elliptic curves over $\Q$ of conductor 2366

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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

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

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Results (32 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2366.a1	2366e1	2366.a	2366e	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{2} \cdot 7^{2} \cdot 13^{4} $	$2$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.8.0.1	3B.1.1	$84$	$32$	$0$	$0.640828752$	$1$		$30$	$1440$	$0.304303$	$-1214950633/196$	$0.94977$	$4.01316$	$[1, 0, 1, -680, 6762]$	$y^2+xy+y=x^3-680x+6762$	3.8.0-3.a.1.2, 4.2.0.a.1, 12.16.0-12.a.1.6, 28.4.0-4.a.1.1, 84.32.0.?	$[(17, 5), (1, 77)]$
2366.a2	2366e2	2366.a	2366e	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{6} \cdot 7^{6} \cdot 13^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.8.0.2	3B.1.2	$84$	$32$	$0$	$0.071203194$	$1$		$32$	$4320$	$0.853609$	$17546087/7529536$	$1.06847$	$4.31815$	$[1, 0, 1, 165, 22310]$	$y^2+xy+y=x^3+165x+22310$	3.8.0-3.a.1.1, 4.2.0.a.1, 12.16.0-12.a.1.5, 28.4.0-4.a.1.1, 84.32.0.?	$[(79, 688), (23, 184)]$
2366.b1	2366b1	2366.b	2366b	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{10} \cdot 7^{2} \cdot 13^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$28$	$4$	$0$	$0.319988094$	$1$		$6$	$6240$	$1.295137$	$15925559/50176$	$0.91331$	$4.96781$	$[1, 0, 1, 4897, 278514]$	$y^2+xy+y=x^3+4897x+278514$	4.2.0.a.1, 28.4.0-4.a.1.1	$[(183, 2612)]$
2366.c1	2366h1	2366.c	2366h	$2$	$5$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7 \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3640$	$48$	$1$	$0.770313082$	$1$		$4$	$240$	$-0.384424$	$-226981/14$	$0.81013$	$2.59092$	$[1, 1, 0, -16, -34]$	$y^2+xy=x^3+x^2-16x-34$	5.6.0.a.1, 65.24.0-65.a.2.3, 280.12.0.?, 728.2.0.?, 3640.48.1.?	$[(5, 4)]$
2366.c2	2366h2	2366.c	2366h	$2$	$5$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{5} \cdot 7^{5} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3640$	$48$	$1$	$0.154062616$	$1$		$6$	$1200$	$0.420295$	$5735339/537824$	$1.00587$	$3.64768$	$[1, 1, 0, 49, 1669]$	$y^2+xy=x^3+x^2+49x+1669$	5.6.0.a.1, 65.24.0-65.a.1.2, 280.12.0.?, 728.2.0.?, 3640.48.1.?	$[(5, 43)]$
2366.d1	2366c4	2366.d	2366c	$4$	$4$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2^{5} \cdot 7^{3} \cdot 13^{14} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$728$	$48$	$0$	$1$	$1$		$0$	$120960$	$2.732483$	$22868021811807457713/8953460393696$	$1.08758$	$7.71866$	$[1, -1, 0, -9993593, 12158301325]$	$y^2+xy=x^3-x^2-9993593x+12158301325$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0.bp.1, 104.24.0.?, $\ldots$	$[]$
2366.d2	2366c3	2366.d	2366c	$4$	$4$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2^{5} \cdot 7^{12} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.15	2B	$728$	$48$	$0$	$1$	$1$		$0$	$120960$	$2.732483$	$3389174547561866673/74853681183008$	$1.05145$	$7.47292$	$[1, -1, 0, -5288633, -4589744691]$	$y^2+xy=x^3-x^2-5288633x-4589744691$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 52.12.0-4.c.1.1, 56.24.0.v.1, $\ldots$	$[]$
2366.d3	2366c2	2366.d	2366c	$4$	$4$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2^{10} \cdot 7^{6} \cdot 13^{10} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.3	2Cs	$728$	$48$	$0$	$1$	$1$		$2$	$60480$	$2.385906$	$8511781274893233/3440817243136$	$1.08472$	$6.70231$	$[1, -1, 0, -718873, 128989485]$	$y^2+xy=x^3-x^2-718873x+128989485$	2.6.0.a.1, 8.12.0.a.1, 28.12.0.b.1, 52.12.0-2.a.1.1, 56.24.0.d.1, $\ldots$	$[]$
2366.d4	2366c1	2366.d	2366c	$4$	$4$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{20} \cdot 7^{3} \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.9	2B	$728$	$48$	$0$	$1$	$1$		$1$	$30240$	$2.039333$	$71903073502287/60782804992$	$1.03131$	$6.08782$	$[1, -1, 0, 146407, 14599469]$	$y^2+xy=x^3-x^2+146407x+14599469$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 14.6.0.b.1, 28.12.0.g.1, $\ldots$	$[]$
2366.e1	2366a3	2366.e	2366a	$3$	$9$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$6552$	$144$	$3$	$11.36052613$	$1$		$0$	$18144$	$1.962933$	$-424962187484640625/182$	$1.05379$	$7.20566$	$[1, 0, 1, -2647051, -1657865324]$	$y^2+xy+y=x^3-2647051x-1657865324$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.2, 117.24.0.?, 168.8.0.?, $\ldots$	$[(2111092/3, 3064092680/3)]$
2366.e2	2366a2	2366.e	2366a	$3$	$9$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{3} \cdot 7^{3} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$6552$	$144$	$3$	$3.786842045$	$1$		$0$	$6048$	$1.413626$	$-795309684625/6028568$	$0.94067$	$5.50971$	$[1, 0, 1, -32621, -2285216]$	$y^2+xy+y=x^3-32621x-2285216$	3.12.0.a.1, 39.24.0-3.a.1.1, 168.24.0.?, 728.2.0.?, 819.72.0.?, $\ldots$	$[(2986/3, 126229/3)]$
2366.e3	2366a1	2366.e	2366a	$3$	$9$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{9} \cdot 7 \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$6552$	$144$	$3$	$1.262280681$	$1$		$2$	$2016$	$0.864320$	$37595375/46592$	$0.87083$	$4.24310$	$[1, 0, 1, 1179, -16560]$	$y^2+xy+y=x^3+1179x-16560$	3.4.0.a.1, 9.12.0.a.1, 39.8.0-3.a.1.1, 117.24.0.?, 168.8.0.?, $\ldots$	$[(66, 558)]$
2366.f1	2366d2	2366.f	2366d	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{3} \cdot 7^{3} \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$168$	$16$	$0$	$1$	$1$		$0$	$5616$	$1.167036$	$-156116857/2744$	$0.89198$	$5.07348$	$[1, 0, 1, -10482, -420132]$	$y^2+xy+y=x^3-10482x-420132$	3.8.0-3.a.1.1, 56.2.0.b.1, 168.16.0.?	$[]$
2366.f2	2366d1	2366.f	2366d	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7 \cdot 13^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$168$	$16$	$0$	$1$	$9$	$3$	$2$	$1872$	$0.617729$	$17303/14$	$0.76938$	$3.89734$	$[1, 0, 1, 503, -2702]$	$y^2+xy+y=x^3+503x-2702$	3.8.0-3.a.1.2, 56.2.0.b.1, 168.16.0.?	$[]$
2366.g1	2366f1	2366.g	2366f	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 7 \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$56$	$2$	$0$	$1$	$25$	$5$	$0$	$59280$	$1.972446$	$-19983597574473/3670016$	$1.02843$	$6.58336$	$[1, -1, 0, -528241, -147664867]$	$y^2+xy=x^3-x^2-528241x-147664867$	56.2.0.b.1	$[]$
2366.h1	2366g1	2366.h	2366g	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7^{3} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$1$	$1$		$0$	$6048$	$0.724618$	$4019679/8918$	$1.11550$	$4.07236$	$[1, -1, 0, 560, -8722]$	$y^2+xy=x^3-x^2+560x-8722$	728.2.0.?	$[]$
2366.i1	2366p1	2366.i	2366p	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{10} \cdot 7^{2} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$364$	$4$	$0$	$0.098443260$	$1$		$8$	$480$	$0.012664$	$15925559/50176$	$0.91331$	$2.98688$	$[1, 0, 0, 29, 129]$	$y^2+xy=x^3+29x+129$	4.2.0.a.1, 364.4.0.?	$[(2, 13)]$
2366.j1	2366j6	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2^{9} \cdot 7^{2} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$6552$	$864$	$21$	$1$	$1$		$0$	$12960$	$1.695576$	$2251439055699625/25088$	$1.06489$	$6.53113$	$[1, 0, 0, -461458, -120693756]$	$y^2+xy=x^3-461458x-120693756$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
2366.j2	2366j5	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{18} \cdot 7 \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$6552$	$864$	$21$	$1$	$1$		$1$	$6480$	$1.349003$	$-548347731625/1835008$	$1.02933$	$5.46092$	$[1, 0, 0, -28818, -1890812]$	$y^2+xy=x^3-28818x-1890812$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
2366.j3	2366j4	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2^{3} \cdot 7^{6} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$6552$	$864$	$21$	$1$	$1$		$0$	$4320$	$1.146269$	$4956477625/941192$	$1.00821$	$4.85440$	$[1, 0, 0, -6003, -147239]$	$y^2+xy=x^3-6003x-147239$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$	$[]$
2366.j4	2366j2	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ 2 \cdot 7^{2} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$6552$	$864$	$21$	$1$	$1$		$0$	$1440$	$0.596963$	$128787625/98$	$0.96763$	$4.38455$	$[1, 0, 0, -1778, 28690]$	$y^2+xy=x^3-1778x+28690$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
2366.j5	2366j1	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{2} \cdot 7 \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$6552$	$864$	$21$	$1$	$1$		$1$	$720$	$0.250390$	$-15625/28$	$1.01712$	$3.40541$	$[1, 0, 0, -88, 636]$	$y^2+xy=x^3-88x+636$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
2366.j6	2366j3	2366.j	2366j	$6$	$18$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{6} \cdot 7^{3} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$6552$	$864$	$21$	$1$	$1$		$1$	$2160$	$0.799696$	$9938375/21952$	$0.98695$	$4.18811$	$[1, 0, 0, 757, -13391]$	$y^2+xy=x^3+757x-13391$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$	$[]$
2366.k1	2366k1	2366.k	2366k	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{2} \cdot 7^{2} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.4.0.1	3B	$1092$	$32$	$0$	$1$	$1$		$0$	$18720$	$1.586779$	$-1214950633/196$	$0.94977$	$5.99408$	$[1, 0, 0, -114839, 14971501]$	$y^2+xy=x^3-114839x+14971501$	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 39.8.0-3.a.1.1, 84.16.0.?, $\ldots$	$[]$
2366.k2	2366k2	2366.k	2366k	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{6} \cdot 7^{6} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 3.4.0.1	3B	$1092$	$32$	$0$	$1$	$1$		$0$	$56160$	$2.136086$	$17546087/7529536$	$1.06847$	$6.29907$	$[1, 0, 0, 27966, 48987652]$	$y^2+xy=x^3+27966x+48987652$	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 39.8.0-3.a.1.2, 84.16.0.?, $\ldots$	$[]$
2366.l1	2366n1	2366.l	2366n	$2$	$5$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7 \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3640$	$48$	$1$	$6.175788981$	$1$		$0$	$3120$	$0.898051$	$-226981/14$	$0.81013$	$4.57184$	$[1, 1, 1, -2792, -60897]$	$y^2+xy+y=x^3+x^2-2792x-60897$	5.6.0.a.1, 65.24.0-65.a.2.2, 280.12.0.?, 728.2.0.?, 3640.48.1.?	$[(22419/2, 3334593/2)]$
2366.l2	2366n2	2366.l	2366n	$2$	$5$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{5} \cdot 7^{5} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3640$	$48$	$1$	$1.235157796$	$1$		$4$	$15600$	$1.702770$	$5735339/537824$	$1.00587$	$5.62860$	$[1, 1, 1, 8193, 3625669]$	$y^2+xy+y=x^3+x^2+8193x+3625669$	5.6.0.a.1, 65.24.0-65.a.1.3, 280.12.0.?, 728.2.0.?, 3640.48.1.?	$[(239, 4274)]$
2366.m1	2366o1	2366.m	2366o	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{11} \cdot 7^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$0.042232810$	$1$		$12$	$51744$	$2.153641$	$-10824513276632329/21926008832$	$0.99602$	$6.73369$	$[1, 0, 0, -778840, 264955456]$	$y^2+xy=x^3-778840x+264955456$	728.2.0.?	$[(534, 916)]$
2366.n1	2366i2	2366.n	2366i	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{3} \cdot 7^{3} \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$432$	$-0.115439$	$-156116857/2744$	$0.89198$	$3.09256$	$[1, 0, 0, -62, -196]$	$y^2+xy=x^3-62x-196$	3.4.0.a.1, 39.8.0-3.a.1.2, 56.2.0.b.1, 168.8.0.?, 2184.16.0.?	$[]$
2366.n2	2366i1	2366.n	2366i	$2$	$3$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2 \cdot 7 \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$1$	$1$		$0$	$144$	$-0.664745$	$17303/14$	$0.76938$	$1.91641$	$[1, 0, 0, 3, -1]$	$y^2+xy=x^3+3x-1$	3.4.0.a.1, 39.8.0-3.a.1.1, 56.2.0.b.1, 168.8.0.?, 2184.16.0.?	$[]$
2366.o1	2366l1	2366.o	2366l	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{7} \cdot 7 \cdot 13^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$728$	$2$	$0$	$1$	$1$		$0$	$23520$	$1.596910$	$-1207949625/332678528$	$1.06089$	$5.46653$	$[1, -1, 1, -3750, 1930933]$	$y^2+xy+y=x^3-x^2-3750x+1930933$	728.2.0.?	$[]$
2366.p1	2366m1	2366.p	2366m	$1$	$1$	$ 2 \cdot 7 \cdot 13^{2} $	$ - 2^{19} \cdot 7 \cdot 13^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$56$	$2$	$0$	$1$	$1$		$0$	$4560$	$0.689971$	$-19983597574473/3670016$	$1.02843$	$4.60244$	$[1, -1, 1, -3126, -66491]$	$y^2+xy+y=x^3-x^2-3126x-66491$	56.2.0.b.1	$[]$

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