LMFDB - Elliptic curves over $\Q$ of conductor 462722

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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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Results (29 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
462722.a1	462722a1	462722.a	462722a	$2$	$3$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{6} \cdot 13^{6} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 9.12.0.2	3B	$17316$	$288$	$6$	$1.000294524$	$1$		$4$	$1327104$	$1.060801$	$-8398297/64$	$0.91223$	$2.95657$	$[1, 0, 1, -7947, 273782]$	$y^2+xy+y=x^3-7947x+273782$	3.4.0.a.1, 4.2.0.a.1, 9.12.0.b.1, 12.16.0.b.1, 36.48.0.b.1, $\ldots$	$[(-25, 688)]$
462722.a2	462722a2	462722.a	462722a	$2$	$3$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{18} \cdot 13^{6} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 9.12.0.2	3B	$17316$	$288$	$6$	$3.000883573$	$1$		$0$	$3981312$	$1.610107$	$212207543/262144$	$0.98476$	$3.21282$	$[1, 0, 1, 23318, 1461852]$	$y^2+xy+y=x^3+23318x+1461852$	3.4.0.a.1, 4.2.0.a.1, 9.12.0.b.1, 12.16.0.b.2, 36.48.0.b.2, $\ldots$	$[(2261/5, 253869/5)]$
462722.b1	462722b2	462722.b	462722b	$2$	$5$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{15} \cdot 13^{3} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3, 5$	3.6.0.1, 5.6.0.1	3Ns, 5B	$57720$	$576$	$17$	$1$	$1$		$0$	$6199200$	$2.106602$	$-1680914269/32768$	$1.02322$	$3.88168$	$[1, 1, 0, -440846, 114360628]$	$y^2+xy=x^3+x^2-440846x+114360628$	3.6.0.b.1, 5.6.0.a.1, 15.72.1.a.1, 24.12.0.bx.1, 39.12.0.a.1, $\ldots$	$[ ]$
462722.b2	462722b1	462722.b	462722b	$2$	$5$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{3} \cdot 13^{3} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3, 5$	3.6.0.1, 5.6.0.1	3Ns, 5B	$57720$	$576$	$17$	$1$	$1$		$0$	$1239840$	$1.301882$	$1331/8$	$0.93577$	$2.97383$	$[1, 1, 0, 4079, -305443]$	$y^2+xy=x^3+x^2+4079x-305443$	3.6.0.b.1, 5.6.0.a.1, 15.72.1.a.2, 24.12.0.bx.1, 39.12.0.a.1, $\ldots$	$[ ]$
462722.c1	462722c1	462722.c	462722c	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{5} \cdot 13^{8} \cdot 37^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$296$	$2$	$0$	$19.78935839$	$1$		$0$	$17072640$	$2.793755$	$1724463/1184$	$0.88144$	$4.33469$	$[1, -1, 0, 3195674, -950196012]$	$y^2+xy=x^3-x^2+3195674x-950196012$	296.2.0.?	$[(11698296169/1681, 1360456454803189/1681)]$
462722.d1	462722d1	462722.d	462722d	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{10} \cdot 13^{10} \cdot 37^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$52$	$16$	$0$	$14.43319907$	$1$		$0$	$143216640$	$3.805931$	$-4652805537/29246464$	$0.96757$	$5.29028$	$[1, -1, 0, -89348726, -1119560271244]$	$y^2+xy=x^3-x^2-89348726x-1119560271244$	4.8.0.b.1, 52.16.0-4.b.1.1	$[(1770481852/19, 74479767582518/19)]$
462722.e1	462722e1	462722.e	462722e	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2 \cdot 13^{4} \cdot 37^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.8.0.1	7B	$26936$	$96$	$2$	$13.50942637$	$1$		$0$	$23901696$	$2.882050$	$-607782291676209/74$	$1.05537$	$5.05686$	$[1, -1, 0, -73847539, 244278350967]$	$y^2+xy=x^3-x^2-73847539x+244278350967$	7.8.0.a.1, 56.16.0-7.a.1.6, 91.24.0.?, 259.16.0.?, 296.2.0.?, $\ldots$	$[(22582957/92, 199362507719/92)]$
462722.e2	462722e2	462722.e	462722e	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{7} \cdot 13^{4} \cdot 37^{13} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.8.0.1	7B	$26936$	$96$	$2$	$94.56598462$	$1$		$0$	$167311872$	$3.855003$	$4918167786495951/12151280273024$	$1.12906$	$5.30795$	$[1, -1, 0, 148259021, 1256313832437]$	$y^2+xy=x^3-x^2+148259021x+1256313832437$	7.8.0.a.1, 56.16.0-7.a.1.8, 91.24.0.?, 259.16.0.?, 296.2.0.?, $\ldots$	$[(3721501281385665580467489400057522659773277/8540518911473888516, 7397841108626976939161091172580962012894656852012431723315841921/8540518911473888516)]$
462722.f1	462722f2	462722.f	462722f	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{14} \cdot 13^{8} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 7$	4.8.0.2, 7.8.0.1	7B	$13468$	$768$	$21$	$54.02194516$	$1$		$0$	$56412720$	$3.284863$	$-38575685889/16384$	$1.08547$	$5.10252$	$[1, -1, 0, -90042809, -328966186899]$	$y^2+xy=x^3-x^2-90042809x-328966186899$	4.8.0.b.1, 7.8.0.a.1, 28.128.5.b.1, 91.24.0.?, 148.16.0.?, $\ldots$	$[(91519241786112230263001570/39501769439, 861453770054877041740509635071976146769/39501769439)]$
462722.f2	462722f1	462722.f	462722f	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{2} \cdot 13^{8} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 7$	4.8.0.2, 7.8.0.1	7B	$13468$	$768$	$21$	$7.717420737$	$1$		$0$	$8058960$	$2.311905$	$351/4$	$1.27279$	$3.90759$	$[1, -1, 0, 187981, 135581161]$	$y^2+xy=x^3-x^2+187981x+135581161$	4.8.0.b.1, 7.8.0.a.1, 28.128.5.b.2, 91.24.0.?, 148.16.0.?, $\ldots$	$[(-28404/11, 11947183/11)]$
462722.g1	462722g3	462722.g	462722g	$3$	$9$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{9} \cdot 13^{7} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$34632$	$144$	$3$	$27.28818283$	$1$		$0$	$50621760$	$3.142319$	$-10730978619193/6656$	$1.02193$	$5.14066$	$[1, 0, 1, -106315200, -421939810290]$	$y^2+xy+y=x^3-106315200x-421939810290$	3.4.0.a.1, 9.12.0.a.1, 104.2.0.?, 117.36.0.?, 312.8.0.?, $\ldots$	$[(13855745344399/24810, 44589134017476553237/24810)]$
462722.g2	462722g2	462722.g	462722g	$3$	$9$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{3} \cdot 13^{9} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$34632$	$144$	$3$	$9.096060943$	$1$		$0$	$16873920$	$2.593014$	$-10218313/17576$	$0.94717$	$4.18357$	$[1, 0, 1, -1045945, -820682588]$	$y^2+xy+y=x^3-1045945x-820682588$	3.12.0.a.1, 104.2.0.?, 117.36.0.?, 312.24.1.?, 888.24.0.?, $\ldots$	$[(769519/6, 671933059/6)]$
462722.g3	462722g1	462722.g	462722g	$3$	$9$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2 \cdot 13^{7} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$34632$	$144$	$3$	$3.032020314$	$1$		$2$	$5624640$	$2.043709$	$12167/26$	$0.84415$	$3.63761$	$[1, 0, 1, 110860, 23322340]$	$y^2+xy+y=x^3+110860x+23322340$	3.4.0.a.1, 9.12.0.a.1, 104.2.0.?, 117.36.0.?, 312.8.0.?, $\ldots$	$[(118, 6109)]$
462722.h1	462722h1	462722.h	462722h	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{2} \cdot 13^{6} \cdot 37^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$1924$	$4$	$0$	$23.47820523$	$1$		$0$	$40919040$	$3.094051$	$-1369/4$	$0.91004$	$4.63941$	$[1, 1, 0, -6598608, -16048732396]$	$y^2+xy=x^3+x^2-6598608x-16048732396$	4.2.0.a.1, 1924.4.0.?	$[(265533262754/3611, 135129791217860032/3611)]$
462722.i1	462722i2	462722.i	462722i	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2 \cdot 13^{13} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.2	7B.6.3	$26936$	$96$	$2$	$1$	$49$	$7$	$0$	$121504320$	$3.377728$	$-1064019559329/125497034$	$1.06269$	$4.97772$	$[1, -1, 1, -49207593, -145760144877]$	$y^2+xy+y=x^3-x^2-49207593x-145760144877$	7.24.0.a.2, 104.2.0.?, 728.48.2.?, 2072.48.0.?, 3367.48.0.?, $\ldots$	$[ ]$
462722.i2	462722i1	462722.i	462722i	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{7} \cdot 13^{7} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.24.0.1	7B.6.1	$26936$	$96$	$2$	$1$	$1$		$0$	$17357760$	$2.404774$	$-2146689/1664$	$0.96784$	$4.02338$	$[1, -1, 1, -621783, 288799983]$	$y^2+xy+y=x^3-x^2-621783x+288799983$	7.24.0.a.1, 104.2.0.?, 728.48.2.?, 2072.48.0.?, 3367.48.0.?, $\ldots$	$[ ]$
462722.j1	462722j1	462722.j	462722j	$2$	$3$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{6} \cdot 13^{6} \cdot 37^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 9.12.0.2	3B	$17316$	$288$	$6$	$1$	$1$		$0$	$49102848$	$2.866261$	$-8398297/64$	$0.91223$	$4.61742$	$[1, 0, 0, -10878787, 13900528641]$	$y^2+xy=x^3-10878787x+13900528641$	3.4.0.a.1, 4.2.0.a.1, 9.12.0.b.1, 12.16.0.b.1, 36.48.0.b.1, $\ldots$	$[ ]$
462722.j2	462722j2	462722.j	462722j	$2$	$3$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{18} \cdot 13^{6} \cdot 37^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.2.0.1, 9.12.0.2	3B	$17316$	$288$	$6$	$1$	$1$		$0$	$147308544$	$3.415565$	$212207543/262144$	$0.98476$	$4.87367$	$[1, 0, 0, 31922998, 73951432996]$	$y^2+xy=x^3+31922998x+73951432996$	3.4.0.a.1, 4.2.0.a.1, 9.12.0.b.1, 12.16.0.b.2, 36.48.0.b.2, $\ldots$	$[ ]$
462722.k1	462722k2	462722.k	462722k	$2$	$5$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{15} \cdot 13^{9} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3, 5$	3.6.0.1, 5.6.0.1	3Ns, 5B	$57720$	$576$	$17$	$2.786132117$	$1$		$2$	$80589600$	$3.389076$	$-1680914269/32768$	$1.02322$	$5.06143$	$[1, 1, 1, -74503062, 251622814867]$	$y^2+xy+y=x^3+x^2-74503062x+251622814867$	3.6.0.b.1, 5.6.0.a.1, 15.72.1.a.1, 24.12.0.bx.1, 39.12.0.a.1, $\ldots$	$[(577, 456687)]$
462722.k2	462722k1	462722.k	462722k	$2$	$5$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{3} \cdot 13^{9} \cdot 37^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3, 5$	3.6.0.1, 5.6.0.1	3Ns, 5B	$57720$	$576$	$17$	$13.93066058$	$1$		$0$	$16117920$	$2.584354$	$1331/8$	$0.93577$	$4.15358$	$[1, 1, 1, 689263, -674504745]$	$y^2+xy+y=x^3+x^2+689263x-674504745$	3.6.0.b.1, 5.6.0.a.1, 15.72.1.a.2, 24.12.0.bx.1, 39.12.0.a.1, $\ldots$	$[(82215373/49, 743681014924/49)]$
462722.l1	462722l2	462722.l	462722l	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{14} \cdot 13^{2} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 7$	4.8.0.2, 7.8.0.1	7B	$13468$	$768$	$21$	$1$	$1$		$0$	$4339440$	$2.002388$	$-38575685889/16384$	$1.08547$	$3.92277$	$[1, -1, 1, -532798, -149611315]$	$y^2+xy+y=x^3-x^2-532798x-149611315$	4.8.0.b.1, 7.8.0.a.1, 28.128.5.b.1, 91.24.0.?, 364.384.21.?, $\ldots$	$[ ]$
462722.l2	462722l1	462722.l	462722l	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{2} \cdot 13^{2} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 7$	4.8.0.2, 7.8.0.1	7B	$13468$	$768$	$21$	$1$	$1$		$0$	$619920$	$1.029430$	$351/4$	$1.27279$	$2.72784$	$[1, -1, 1, 1112, 61455]$	$y^2+xy+y=x^3-x^2+1112x+61455$	4.8.0.b.1, 7.8.0.a.1, 28.128.5.b.2, 91.24.0.?, 364.384.21.?, $\ldots$	$[ ]$
462722.m1	462722m1	462722.m	462722m	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2 \cdot 13^{10} \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$1$		$0$	$310722048$	$4.164520$	$-607782291676209/74$	$1.05537$	$6.23661$	$[1, -1, 1, -12480234123, 536642096372165]$	$y^2+xy+y=x^3-x^2-12480234123x+536642096372165$	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 728.48.0.?, 2072.16.0.?, $\ldots$	$[ ]$
462722.m2	462722m2	462722.m	462722m	$2$	$7$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{7} \cdot 13^{10} \cdot 37^{13} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$1$		$0$	$2175054336$	$5.137474$	$4918167786495951/12151280273024$	$1.12906$	$6.48770$	$[1, -1, 1, 25055774517, 2760196657187675]$	$y^2+xy+y=x^3-x^2+25055774517x+2760196657187675$	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 728.48.0.?, 2072.16.0.?, $\ldots$	$[ ]$
462722.n1	462722n1	462722.n	462722n	$2$	$2$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ 2^{4} \cdot 13^{7} \cdot 37^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.23	2B	$3848$	$48$	$0$	$1$	$1$		$1$	$14708736$	$2.568161$	$72511713/7696$	$0.84804$	$4.22805$	$[1, -1, 1, -2009949, -990626347]$	$y^2+xy+y=x^3-x^2-2009949x-990626347$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.1, 962.6.0.?, 1924.24.0.?, $\ldots$	$[ ]$
462722.n2	462722n2	462722.n	462722n	$2$	$2$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{2} \cdot 13^{8} \cdot 37^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.6	2B	$3848$	$48$	$0$	$1$	$4$	$2$	$0$	$29417472$	$2.914734$	$160103007/925444$	$0.87670$	$4.45711$	$[1, -1, 1, 2617271, -4886745587]$	$y^2+xy+y=x^3-x^2+2617271x-4886745587$	2.3.0.a.1, 4.12.0-4.a.1.2, 1924.24.0.?, 3848.48.0.?	$[ ]$
462722.o1	462722o1	462722.o	462722o	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{10} \cdot 13^{10} \cdot 37^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$1924$	$16$	$0$	$1$	$1$		$0$	$3870720$	$2.000473$	$-4652805537/29246464$	$0.96757$	$3.62944$	$[1, -1, 1, -65266, -22086671]$	$y^2+xy+y=x^3-x^2-65266x-22086671$	4.8.0.b.1, 1924.16.0.?	$[ ]$
462722.p1	462722p1	462722.p	462722p	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{5} \cdot 13^{2} \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$296$	$2$	$0$	$1$	$1$		$0$	$1313280$	$1.511282$	$1724463/1184$	$0.88144$	$3.15494$	$[1, -1, 1, 18909, -436861]$	$y^2+xy+y=x^3-x^2+18909x-436861$	296.2.0.?	$[ ]$
462722.q1	462722q1	462722.q	462722q	$1$	$1$	$ 2 \cdot 13^{2} \cdot 37^{2} $	$ - 2^{2} \cdot 13^{6} \cdot 37^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$52$	$4$	$0$	$1$	$1$		$0$	$1105920$	$1.288593$	$-1369/4$	$0.91004$	$2.97857$	$[1, 1, 1, -4820, -318791]$	$y^2+xy+y=x^3+x^2-4820x-318791$	4.2.0.a.1, 52.4.0-4.a.1.1	$[ ]$

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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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