LMFDB - Elliptic curves over $\Q$ of conductor 4598

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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 (27 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
4598.a1	4598k2	4598.a	4598k	$2$	$5$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{6} \cdot 19^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$8360$	$48$	$1$	$0.169204710$	$1$	$6$	$14000$	$1.216732$	$-37966934881/4952198$	$0.97714$	$4.61863$	$[1, 1, 0, -8472, 328750]$	$y^2+xy=x^3+x^2-8472x+328750$	5.12.0.a.2, 55.24.0-5.a.2.1, 152.2.0.?, 760.24.1.?, 8360.48.1.?	$[(127, 1086)]$
4598.a2	4598k1	4598.a	4598k	$2$	$5$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{5} \cdot 11^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$8360$	$48$	$1$	$0.846023550$	$1$	$4$	$2800$	$0.412013$	$-1/608$	$1.37833$	$3.35005$	$[1, 1, 0, -2, -1580]$	$y^2+xy=x^3+x^2-2x-1580$	5.12.0.a.1, 55.24.0-5.a.1.1, 152.2.0.?, 760.24.1.?, 8360.48.1.?	$[(17, 52)]$
4598.b1	4598f1	4598.b	4598f	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{13} \cdot 11^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$12480$	$1.284218$	$31764658463/18833408$	$0.95180$	$4.57337$	$[1, 1, 0, 7984, 46336]$	$y^2+xy=x^3+x^2+7984x+46336$	152.2.0.?	$[]$
4598.c1	4598j1	4598.c	4598j	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{19} \cdot 11^{8} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$16.11801635$	$1$	$0$	$20064$	$1.645243$	$-18396908233/9961472$	$0.92165$	$5.15559$	$[1, 1, 0, -32914, -3211468]$	$y^2+xy=x^3+x^2-32914x-3211468$	152.2.0.?	$[(8613961/111, 23837648069/111)]$
4598.d1	4598c1	4598.d	4598c	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{2} \cdot 11^{10} \cdot 19^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.8.0.2		$44$	$16$	$0$	$1$	$1$	$0$	$89760$	$2.282269$	$-84985354223649/521284$	$1.03261$	$6.64650$	$[1, -1, 0, -2711330, 1719076904]$	$y^2+xy=x^3-x^2-2711330x+1719076904$	4.8.0.b.1, 44.16.0-4.b.1.1	$[]$
4598.e1	4598b1	4598.e	4598b	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$7128$	$1.208059$	$-48077951625/38$	$0.99821$	$5.19119$	$[1, -1, 0, -45337, -3704277]$	$y^2+xy=x^3-x^2-45337x-3704277$	152.2.0.?	$[]$
4598.f1	4598d1	4598.f	4598d	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ 2^{2} \cdot 11^{7} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$1672$	$12$	$0$	$1$	$1$	$1$	$2400$	$0.483764$	$5545233/836$	$0.95410$	$3.54731$	$[1, -1, 0, -446, -3008]$	$y^2+xy=x^3-x^2-446x-3008$	2.3.0.a.1, 8.6.0.d.1, 418.6.0.?, 1672.12.0.?	$[]$
4598.f2	4598d2	4598.f	4598d	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{8} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$1672$	$12$	$0$	$1$	$1$	$0$	$4800$	$0.830338$	$27818127/87362$	$0.93206$	$3.91495$	$[1, -1, 0, 764, -17286]$	$y^2+xy=x^3-x^2+764x-17286$	2.3.0.a.1, 8.6.0.a.1, 836.6.0.?, 1672.12.0.?	$[]$
4598.g1	4598e1	4598.g	4598e	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{7} \cdot 11^{2} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$840$	$-0.270434$	$101871/2432$	$1.11843$	$2.37419$	$[1, -1, 0, 5, -27]$	$y^2+xy=x^3-x^2+5x-27$	152.2.0.?	$[]$
4598.h1	4598i1	4598.h	4598i	$2$	$3$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{8} \cdot 19 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$456$	$16$	$0$	$7.360780789$	$1$	$2$	$3168$	$0.648151$	$-471625/38$	$0.76327$	$3.83920$	$[1, 0, 1, -971, 12340]$	$y^2+xy+y=x^3-971x+12340$	3.8.0-3.a.1.2, 152.2.0.?, 456.16.0.?	$[(-26/7, 38809/7)]$
4598.h2	4598i2	4598.h	4598i	$2$	$3$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{3} \cdot 11^{8} \cdot 19^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$456$	$16$	$0$	$2.453593596$	$1$	$2$	$9504$	$1.197458$	$94766375/54872$	$1.02664$	$4.45256$	$[1, 0, 1, 5684, 4354]$	$y^2+xy+y=x^3+5684x+4354$	3.8.0-3.a.1.1, 152.2.0.?, 456.16.0.?	$[(14, 287)]$
4598.i1	4598a2	4598.i	4598a	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ 2^{2} \cdot 11^{9} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1$	$1$	$0$	$23232$	$1.312813$	$1134626507/1444$	$0.89450$	$5.03127$	$[1, 1, 0, -28921, -1903095]$	$y^2+xy=x^3+x^2-28921x-1903095$	2.3.0.a.1, 44.6.0.a.1, 76.6.0.?, 836.12.0.?	$[]$
4598.i2	4598a1	4598.i	4598a	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ 2^{4} \cdot 11^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1$	$1$	$1$	$11616$	$0.966239$	$571787/304$	$0.84290$	$4.13092$	$[1, 1, 0, -2301, -13075]$	$y^2+xy=x^3+x^2-2301x-13075$	2.3.0.a.1, 44.6.0.b.1, 76.6.0.?, 418.6.0.?, 836.12.0.?	$[]$
4598.j1	4598h1	4598.j	4598h	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$6720$	$0.621765$	$-20346417/4598$	$0.81889$	$3.74055$	$[1, -1, 0, -688, 8366]$	$y^2+xy=x^3-x^2-688x+8366$	152.2.0.?	$[]$
4598.k1	4598g1	4598.k	4598g	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{7} \cdot 11^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$16632$	$1.026562$	$-81563625/2432$	$1.12953$	$4.44072$	$[1, -1, 0, -5407, 158285]$	$y^2+xy=x^3-x^2-5407x+158285$	152.2.0.?	$[]$
4598.l1	4598o1	4598.l	4598o	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{19} \cdot 11^{2} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$0.175832775$	$1$	$6$	$1824$	$0.446295$	$-18396908233/9961472$	$0.92165$	$3.44959$	$[1, 1, 1, -272, 2289]$	$y^2+xy+y=x^3+x^2-272x+2289$	152.2.0.?	$[(-11, 69)]$
4598.m1	4598q1	4598.m	4598q	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{2} \cdot 11^{4} \cdot 19^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	4.16.0.2		$4$	$16$	$0$	$1$	$1$	$0$	$8160$	$1.083321$	$-84985354223649/521284$	$1.03261$	$4.94050$	$[1, -1, 1, -22408, -1285457]$	$y^2+xy+y=x^3-x^2-22408x-1285457$	4.16.0-4.b.1.1	$[]$
4598.n1	4598p1	4598.n	4598p	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{2} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$648$	$0.009113$	$-48077951625/38$	$0.99821$	$3.48519$	$[1, -1, 1, -375, 2885]$	$y^2+xy+y=x^3-x^2-375x+2885$	152.2.0.?	$[]$
4598.o1	4598r1	4598.o	4598r	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{7} \cdot 11^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$9240$	$0.928514$	$101871/2432$	$1.11843$	$4.08019$	$[1, -1, 1, 582, 34169]$	$y^2+xy+y=x^3-x^2+582x+34169$	152.2.0.?	$[]$
4598.p1	4598n3	4598.p	4598n	$3$	$9$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{27} \cdot 11^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$45144$	$1296$	$43$	$0.315644550$	$1$	$6$	$19440$	$1.684116$	$-69173457625/2550136832$	$1.05462$	$5.16010$	$[1, 0, 0, -10348, 3258256]$	$y^2+xy=x^3-10348x+3258256$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 33.8.0-3.a.1.1, 99.24.0.?, $\ldots$	$[(120, 1876)]$
4598.p2	4598n1	4598.p	4598n	$3$	$9$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{3} \cdot 11^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$45144$	$1296$	$43$	$2.840800951$	$1$	$2$	$2160$	$0.585505$	$-413493625/152$	$0.93281$	$4.05865$	$[1, 0, 0, -1878, -31492]$	$y^2+xy=x^3-1878x-31492$	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 33.8.0-3.a.1.2, 99.24.0.?, $\ldots$	$[(274, 4340)]$
4598.p3	4598n2	4598.p	4598n	$3$	$9$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{9} \cdot 11^{6} \cdot 19^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.36.0.2	3Cs	$45144$	$1296$	$43$	$0.946933650$	$1$	$4$	$6480$	$1.134811$	$94196375/3511808$	$1.01875$	$4.37524$	$[1, 0, 0, 1147, -118975]$	$y^2+xy=x^3+1147x-118975$	3.12.0.a.1, 9.36.0.b.1, 33.24.0-3.a.1.1, 99.72.0.?, 152.2.0.?, $\ldots$	$[(98, 919)]$
4598.q1	4598m1	4598.q	4598m	$2$	$3$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2 \cdot 11^{2} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$5016$	$16$	$0$	$4.392967045$	$1$	$0$	$288$	$-0.550797$	$-471625/38$	$0.76327$	$2.13320$	$[1, 0, 0, -8, -10]$	$y^2+xy=x^3-8x-10$	3.4.0.a.1, 33.8.0-3.a.1.2, 152.2.0.?, 456.8.0.?, 5016.16.0.?	$[(53/4, -3/4)]$
4598.q2	4598m2	4598.q	4598m	$2$	$3$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{3} \cdot 11^{2} \cdot 19^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$5016$	$16$	$0$	$1.464322348$	$1$	$4$	$864$	$-0.001490$	$94766375/54872$	$1.02664$	$2.74655$	$[1, 0, 0, 47, 1]$	$y^2+xy=x^3+47x+1$	3.4.0.a.1, 33.8.0-3.a.1.1, 152.2.0.?, 456.8.0.?, 5016.16.0.?	$[(0, 1)]$
4598.r1	4598l2	4598.r	4598l	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ 2^{2} \cdot 11^{3} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1$	$1$	$0$	$2112$	$0.113865$	$1134626507/1444$	$0.89450$	$3.32527$	$[1, 1, 1, -239, 1321]$	$y^2+xy+y=x^3+x^2-239x+1321$	2.3.0.a.1, 44.6.0.a.1, 76.6.0.?, 836.12.0.?	$[]$
4598.r2	4598l1	4598.r	4598l	$2$	$2$	$ 2 \cdot 11^{2} \cdot 19 $	$ 2^{4} \cdot 11^{3} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$836$	$12$	$0$	$1$	$1$	$1$	$1056$	$-0.232708$	$571787/304$	$0.84290$	$2.42491$	$[1, 1, 1, -19, 1]$	$y^2+xy+y=x^3+x^2-19x+1$	2.3.0.a.1, 44.6.0.b.1, 76.6.0.?, 418.6.0.?, 836.12.0.?	$[]$
4598.s1	4598s1	4598.s	4598s	$1$	$1$	$ 2 \cdot 11^{2} \cdot 19 $	$ - 2^{7} \cdot 11^{2} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1$	$1$	$0$	$1512$	$-0.172386$	$-81563625/2432$	$1.12953$	$2.73472$	$[1, -1, 1, -45, -107]$	$y^2+xy+y=x^3-x^2-45x-107$	152.2.0.?	$[]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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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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