LMFDB - Elliptic curves over $\Q$ of conductor 180708

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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 (20 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
180708.a1	180708c2	180708.a	180708c	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{8} \cdot 3^{7} \cdot 11^{4} \cdot 37^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$		$1$	$29417472$	$3.072212$	$983758169579344/43835197923$	$0.92785$	$5.09995$	$[0, -1, 0, -18011020, 28271522056]$	$y^2=x^3-x^2-18011020x+28271522056$	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[]$
180708.a2	180708c1	180708.a	180708c	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{4} \cdot 3^{14} \cdot 11^{2} \cdot 37^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$		$1$	$14708736$	$2.725639$	$75760866033664/21413352213$	$1.06331$	$4.65910$	$[0, -1, 0, -3041005, -1458927734]$	$y^2=x^3-x^2-3041005x-1458927734$	2.3.0.a.1, 12.6.0.b.1, 74.6.0.?, 444.12.0.?	$[]$
180708.b1	180708d1	180708.b	180708d	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{2} \cdot 11^{2} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$9768$	$4$	$0$	$0.525550130$	$1$		$6$	$67392$	$0.325642$	$-592/1089$	$1.19792$	$2.24832$	$[0, -1, 0, -12, -936]$	$y^2=x^3-x^2-12x-936$	4.2.0.a.1, 9768.4.0.?	$[(18, 66)]$
180708.c1	180708e1	180708.c	180708e	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 11^{5} \cdot 37^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$0.533020378$	$1$		$4$	$30689280$	$3.459019$	$-4075934708727808/13045131$	$1.03285$	$5.81400$	$[0, -1, 0, -321207557, 2215893745761]$	$y^2=x^3-x^2-321207557x+2215893745761$	22.2.0.a.1	$[(9127, 210826)]$
180708.d1	180708f2	180708.d	180708f	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{8} \cdot 3^{5} \cdot 11^{2} \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$3041280$	$2.220821$	$932410994128/29403$	$0.99766$	$4.52485$	$[0, -1, 0, -1769204, 906329160]$	$y^2=x^3-x^2-1769204x+906329160$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[]$
180708.d2	180708f1	180708.d	180708f	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{4} \cdot 3^{10} \cdot 11 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$1520640$	$1.874249$	$-3196715008/649539$	$1.08791$	$3.85178$	$[0, -1, 0, -105869, 15446934]$	$y^2=x^3-x^2-105869x+15446934$	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[]$
180708.e1	180708g1	180708.e	180708g	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 11 \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.592877612$	$1$		$2$	$72576$	$0.313348$	$303104/891$	$0.79216$	$2.21360$	$[0, -1, 0, 99, 729]$	$y^2=x^3-x^2+99x+729$	22.2.0.a.1	$[(0, 27)]$
180708.f1	180708h1	180708.f	180708h	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{16} \cdot 11 \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$112.2585602$	$1$		$0$	$13271040$	$3.011101$	$-1852044335558653867196416/473513931$	$1.12434$	$5.67100$	$[0, -1, 0, -180380821, -932407265183]$	$y^2=x^3-x^2-180380821x-932407265183$	22.2.0.a.1	$[(5096204582240585140157252620090011124912483995024/8572059622641394763111, 11270308031178162076704029625044028286467300839142062905055687126169297551/8572059622641394763111)]$
180708.g1	180708i2	180708.g	180708i	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{8} \cdot 3^{5} \cdot 11^{2} \cdot 37^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$6.794268796$	$1$		$3$	$15759360$	$3.246803$	$1666315860501346000/40252707$	$1.07171$	$5.71416$	$[0, -1, 0, -214697988, 1210920788808]$	$y^2=x^3-x^2-214697988x+1210920788808$	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[(13502, 879406)]$
180708.g2	180708i1	180708.g	180708i	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{4} \cdot 3^{10} \cdot 11^{4} \cdot 37^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$3.397134398$	$1$		$5$	$7879680$	$2.900230$	$6532108386304000/31987847133$	$1.30184$	$5.02730$	$[0, -1, 0, -13434453, 18877123710]$	$y^2=x^3-x^2-13434453x+18877123710$	2.3.0.a.1, 12.6.0.b.1, 74.6.0.?, 444.12.0.?	$[(-1557, 189783)]$
180708.h1	180708j2	180708.h	180708j	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{8} \cdot 3 \cdot 11^{4} \cdot 37^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$		$1$	$6303744$	$2.526154$	$1482435250000/60130587$	$0.92845$	$4.56316$	$[0, -1, 0, -2064908, -1100646744]$	$y^2=x^3-x^2-2064908x-1100646744$	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[]$
180708.h2	180708j1	180708.h	180708j	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 37^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$		$1$	$3151872$	$2.179577$	$23018340352000/40293$	$1.07901$	$4.56068$	$[0, -1, 0, -2044373, -1124409846]$	$y^2=x^3-x^2-2044373x-1124409846$	2.3.0.a.1, 12.6.0.b.1, 74.6.0.?, 444.12.0.?	$[]$
180708.i1	180708k1	180708.i	180708k	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 11 \cdot 37^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.430068706$	$1$		$2$	$2685312$	$2.118809$	$303104/891$	$0.79216$	$4.00345$	$[0, -1, 0, 135075, 38548809]$	$y^2=x^3-x^2+135075x+38548809$	22.2.0.a.1	$[(3651, 221778)]$
180708.j1	180708l1	180708.j	180708l	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{16} \cdot 11 \cdot 37^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$139.5307188$	$1$		$0$	$491028480$	$4.816559$	$-1852044335558653867196416/473513931$	$1.12434$	$7.46085$	$[0, -1, 0, -246941344405, -47232188499445487]$	$y^2=x^3-x^2-246941344405x-47232188499445487$	22.2.0.a.1	$[(1008368676924885738791175762155157863330249162722993568120751399/27762715951920215446548818921, 29253318888969995068764595505552551190670515015276850642089868301078074021733369712164143935594/27762715951920215446548818921)]$
180708.k1	180708m1	180708.k	180708m	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{2} \cdot 11^{2} \cdot 37^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.2.0.1		$264$	$4$	$0$	$16.06938759$	$1$		$0$	$2493504$	$2.131100$	$-592/1089$	$1.19792$	$4.03817$	$[0, -1, 0, -16884, -47611944]$	$y^2=x^3-x^2-16884x-47611944$	4.2.0.a.1, 264.4.0.?	$[(37015665/263, 178539470538/263)]$
180708.l1	180708n1	180708.l	180708n	$1$	$1$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 11^{5} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$22$	$2$	$0$	$1.310195726$	$1$		$2$	$829440$	$1.653561$	$-4075934708727808/13045131$	$1.03285$	$4.02415$	$[0, -1, 0, -234629, 43822641]$	$y^2=x^3-x^2-234629x+43822641$	22.2.0.a.1	$[(280, 11)]$
180708.m1	180708a2	180708.m	180708a	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{8} \cdot 3 \cdot 11^{2} \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$580608$	$1.454165$	$810448/363$	$0.86847$	$3.37193$	$[0, 1, 0, -16884, -407100]$	$y^2=x^3+x^2-16884x-407100$	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[]$
180708.m2	180708a1	180708.m	180708a	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{4} \cdot 3^{2} \cdot 11 \cdot 37^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$290304$	$1.107592$	$131072/99$	$1.36072$	$2.99237$	$[0, 1, 0, 3651, -45684]$	$y^2=x^3+x^2+3651x-45684$	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[]$
180708.n1	180708b1	180708.n	180708b	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ 2^{4} \cdot 3^{8} \cdot 11^{4} \cdot 37^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$3256$	$48$	$0$	$1$	$1$		$1$	$25214976$	$3.178158$	$17453395699253248/4865706969453$	$0.99749$	$5.10849$	$[0, 1, 0, -18642129, -22309384680]$	$y^2=x^3+x^2-18642129x-22309384680$	2.3.0.a.1, 4.6.0.b.1, 74.6.0.?, 88.12.0.?, 148.24.0.?, $\ldots$	$[]$
180708.n2	180708b2	180708.n	180708b	$2$	$2$	$ 2^{2} \cdot 3 \cdot 11 \cdot 37^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 11^{2} \cdot 37^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$3256$	$48$	$0$	$1$	$4$	$2$	$1$	$50429952$	$3.524734$	$19144301716363952/25146684534609$	$0.96435$	$5.36491$	$[0, 1, 0, 48445716, -146234051964]$	$y^2=x^3+x^2+48445716x-146234051964$	2.3.0.a.1, 4.6.0.a.1, 88.12.0.?, 148.12.0.?, 296.24.0.?, $\ldots$	$[]$

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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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