LMFDB - Elliptic curves over $\Q$ of conductor 17661

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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

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
17661.a1	17661d1	17661.a	17661d	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{3} \cdot 7 \cdot 29^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$42$	$2$	$0$	$5.137516039$	$1$	$2$	$41760$	$1.389997$	$707281/189$	$0.99552$	$4.13203$	$[1, 1, 1, -14735, 498944]$	$y^2+xy+y=x^3+x^2-14735x+498944$	42.2.0.a.1	$[(-76, 1127)]$
17661.b1	17661i1	17661.b	17661i	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{11} \cdot 7^{13} \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$42$	$2$	$0$	$0.107243177$	$1$	$8$	$686400$	$2.412453$	$170295687079857398473/17163597526568829$	$1.04199$	$5.45230$	$[1, 0, 0, -1089997, 397955876]$	$y^2+xy=x^3-1089997x+397955876$	42.2.0.a.1	$[(-229, 25325)]$
17661.c1	17661g2	17661.c	17661g	$2$	$2$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{2} \cdot 7 \cdot 29^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2436$	$12$	$0$	$2.723719473$	$1$	$2$	$53760$	$1.405912$	$4956477625/52983$	$0.86867$	$4.34883$	$[1, 0, 0, -29873, 1966386]$	$y^2+xy=x^3-29873x+1966386$	2.3.0.a.1, 28.6.0.a.1, 348.6.0.?, 2436.12.0.?	$[(447, 8607)]$
17661.c2	17661g1	17661.c	17661g	$2$	$2$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3 \cdot 7^{2} \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2436$	$12$	$0$	$5.447438947$	$1$	$1$	$26880$	$1.059340$	$-15625/4263$	$0.95144$	$3.68319$	$[1, 0, 0, -438, 76659]$	$y^2+xy=x^3-438x+76659$	2.3.0.a.1, 28.6.0.b.1, 174.6.0.?, 2436.12.0.?	$[(-71/3, 7726/3)]$
17661.d1	17661h1	17661.d	17661h	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3^{3} \cdot 7 \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$84$	$2$	$0$	$1.607166442$	$1$	$2$	$1800$	$-0.236672$	$-4317433/189$	$0.81869$	$2.25845$	$[1, 0, 0, -32, -75]$	$y^2+xy=x^3-32x-75$	84.2.0.?	$[(7, 4)]$
17661.e1	17661c1	17661.e	17661c	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{11} \cdot 7^{13} \cdot 29^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$42$	$2$	$0$	$4.797543316$	$1$	$2$	$19905600$	$4.096100$	$170295687079857398473/17163597526568829$	$1.04199$	$7.51831$	$[1, 1, 0, -916687494, 9707579234739]$	$y^2+xy=x^3+x^2-916687494x+9707579234739$	42.2.0.a.1	$[(5366, 2220643)]$
17661.f1	17661a5	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3 \cdot 7^{2} \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$9744$	$192$	$1$	$18.05542860$	$1$	$0$	$100352$	$1.757853$	$53297461115137/147$	$1.05087$	$5.29810$	$[1, 1, 0, -659361, -206353626]$	$y^2+xy=x^3+x^2-659361x-206353626$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[(1359305069/1180, 14033151219543/1180)]$
17661.f2	17661a3	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{2} \cdot 7^{4} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.18	2Cs	$4872$	$192$	$1$	$9.027714301$	$1$	$2$	$50176$	$1.411280$	$13027640977/21609$	$1.08149$	$4.44765$	$[1, 1, 0, -41226, -3234465]$	$y^2+xy=x^3+x^2-41226x-3234465$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$	$[(194549/20, 74815103/20)]$
17661.f3	17661a4	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{8} \cdot 7 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.88	2B	$9744$	$192$	$1$	$2.256928575$	$1$	$2$	$50176$	$1.411280$	$6570725617/45927$	$1.00160$	$4.37766$	$[1, 1, 0, -32816, 2260629]$	$y^2+xy=x^3+x^2-32816x+2260629$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[(292, 4059)]$
17661.f4	17661a6	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3 \cdot 7^{8} \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.90	2B	$9744$	$192$	$1$	$18.05542860$	$1$	$0$	$100352$	$1.757853$	$-4354703137/17294403$	$1.04266$	$4.54647$	$[1, 1, 0, -28611, -5235204]$	$y^2+xy=x^3+x^2-28611x-5235204$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[(1597140269/1820, 56796050222813/1820)]$
17661.f5	17661a2	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{4} \cdot 7^{2} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.10	2Cs	$4872$	$192$	$1$	$4.513857150$	$1$	$2$	$25088$	$1.064707$	$7189057/3969$	$1.14862$	$3.68048$	$[1, 1, 0, -3381, -17640]$	$y^2+xy=x^3+x^2-3381x-17640$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[(-49/2, 1239/2)]$
17661.f6	17661a1	17661.f	17661a	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3^{2} \cdot 7 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.1	2B	$9744$	$192$	$1$	$2.256928575$	$1$	$3$	$12544$	$0.718133$	$103823/63$	$0.97868$	$3.24715$	$[1, 1, 0, 824, -1661]$	$y^2+xy=x^3+x^2+824x-1661$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[(466, 9859)]$
17661.g1	17661b1	17661.g	17661b	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3^{3} \cdot 7 \cdot 29^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$84$	$2$	$0$	$10.64603080$	$1$	$0$	$52200$	$1.446976$	$-4317433/189$	$0.81869$	$4.32447$	$[1, 1, 0, -26929, -1775330]$	$y^2+xy=x^3+x^2-26929x-1775330$	84.2.0.?	$[(3261330/71, 5567200390/71)]$
17661.h1	17661f4	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{3} \cdot 7^{2} \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.3	2B	$9744$	$192$	$1$	$7.645746051$	$1$	$0$	$1290240$	$2.974308$	$947531277805646290177/38367$	$1.01996$	$7.00515$	$[1, 0, 1, -172088802, 868900127401]$	$y^2+xy+y=x^3-172088802x+868900127401$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0-8.n.1.5, $\ldots$	$[(424781/4, 247128507/4)]$
17661.h2	17661f5	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{24} \cdot 7 \cdot 29^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.89	2B	$9744$	$192$	$1$	$3.822873025$	$1$	$0$	$2580480$	$3.320885$	$8471112631466271697/1662662681263647$	$1.00847$	$6.52278$	$[1, 0, 1, -35716447, -66790896769]$	$y^2+xy+y=x^3-35716447x-66790896769$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 28.12.0.h.1, 48.48.0-48.e.2.25, $\ldots$	$[(195499/5, 44947897/5)]$
17661.h3	17661f3	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{12} \cdot 7^{2} \cdot 29^{10} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.17	2Cs	$4872$	$192$	$1$	$7.645746051$	$1$	$2$	$1290240$	$2.974308$	$244883173420511137/18418027974129$	$1.08831$	$6.16041$	$[1, 0, 1, -10961612, 13028593205]$	$y^2+xy+y=x^3-10961612x+13028593205$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 24.48.0-24.i.1.8, 28.24.0.c.1, $\ldots$	$[(101787/2, 32109479/2)]$
17661.h4	17661f2	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{6} \cdot 7^{4} \cdot 29^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.9	2Cs	$4872$	$192$	$1$	$3.822873025$	$1$	$4$	$645120$	$2.627735$	$231331938231569617/1472026689$	$0.98909$	$6.15459$	$[1, 0, 1, -10755567, 13575848725]$	$y^2+xy+y=x^3-10755567x+13575848725$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 12.24.0-4.b.1.2, 24.48.0-24.i.2.23, $\ldots$	$[(25445, 4013985)]$
17661.h5	17661f1	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3^{3} \cdot 7^{8} \cdot 29^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.87	2B	$9744$	$192$	$1$	$1.911436512$	$1$	$3$	$322560$	$2.281162$	$-53297461115137/4513839183$	$0.94722$	$5.31206$	$[1, 0, 1, -659362, 220588751]$	$y^2+xy+y=x^3-659362x+220588751$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 24.48.0-24.bz.1.10, $\ldots$	$[(427, 3902)]$
17661.h6	17661f6	17661.h	17661f	$6$	$8$	$ 3 \cdot 7 \cdot 29^{2} $	$ - 3^{6} \cdot 7 \cdot 29^{14} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.14	2B	$9744$	$192$	$1$	$15.29149210$	$1$	$0$	$2580480$	$3.320885$	$215015459663151503/2552757445339983$	$1.02586$	$6.45094$	$[1, 0, 1, 10496503, 57824554079]$	$y^2+xy+y=x^3+10496503x+57824554079$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0-8.n.1.6, $\ldots$	$[(17080899/26, 71075324195/26)]$
17661.i1	17661e1	17661.i	17661e	$1$	$1$	$ 3 \cdot 7 \cdot 29^{2} $	$ 3^{3} \cdot 7 \cdot 29^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$42$	$2$	$0$	$0.862927255$	$1$	$2$	$1440$	$-0.293650$	$707281/189$	$0.99552$	$2.06601$	$[1, 0, 1, -18, 19]$	$y^2+xy+y=x^3-18x+19$	42.2.0.a.1	$[(-1, 6)]$

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Elliptic curves over $\Q$
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Genus 2 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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