LMFDB - Elliptic curve search results

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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 (23 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	Semistable	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
3570.b2	3570a1	3570.b	3570a	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.6.0.1	2B	$952$	$12$	$0$	$3.024234151$	$1$	$5$	$7680$	$1.036938$	$-527690404915129/1782829440000$	$0.95803$	$4.37905$	$[1, 1, 0, -1683, -70227]$	$y^2+xy=x^3+x^2-1683x-70227$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(86, 613)]$
10710.bh2	10710bj1	10710.bh	10710bj	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.138917126$	$1$	$17$	$61440$	$1.586243$	$-527690404915129/1782829440000$	$0.95803$	$4.57097$	$[1, -1, 1, -15152, 1880979]$	$y^2+xy+y=x^3-x^2-15152x+1880979$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-103, 1581)]$
17850.cg2	17850cd1	17850.cg	17850cd	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.508491567$	$1$	$11$	$184320$	$1.841656$	$-527690404915129/1782829440000$	$0.95803$	$4.64554$	$[1, 0, 0, -42088, -8694208]$	$y^2+xy=x^3-42088x-8694208$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(512, 9944)]$
24990.bh2	24990bi1	24990.bh	24990bi	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{7} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.407435353$	$1$	$11$	$368640$	$2.009892$	$-527690404915129/1782829440000$	$0.95803$	$4.69054$	$[1, 0, 1, -82493, 23840408]$	$y^2+xy+y=x^3-82493x+23840408$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(99, 4030)]$
28560.cw2	28560dk1	28560.cw	28560dk	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{22} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$184320$	$1.730083$	$-527690404915129/1782829440000$	$0.95803$	$4.30223$	$[0, 1, 0, -26936, 4440660]$	$y^2=x^3+x^2-26936x+4440660$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
53550.bn2	53550bo1	53550.bn	53550bo	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{10} \cdot 3^{10} \cdot 5^{10} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$2.548578876$	$1$	$5$	$1474560$	$2.390961$	$-527690404915129/1782829440000$	$0.95803$	$4.78220$	$[1, -1, 0, -378792, 234743616]$	$y^2+xy=x^3-x^2-378792x+234743616$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-336, 18168)]$
60690.be2	60690be1	60690.be	60690be	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$2211840$	$2.453545$	$-527690404915129/1782829440000$	$0.95803$	$4.79604$	$[1, 0, 1, -486538, -341619844]$	$y^2+xy+y=x^3-486538x-341619844$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
74970.cd2	74970co1	74970.cd	74970co	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{7} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$2949120$	$2.559196$	$-527690404915129/1782829440000$	$0.95803$	$4.81870$	$[1, -1, 1, -742433, -643691023]$	$y^2+xy+y=x^3-x^2-742433x-643691023$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
85680.fs2	85680fu1	85680.fs	85680fu	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{22} \cdot 3^{10} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$1474560$	$2.279392$	$-527690404915129/1782829440000$	$0.95803$	$4.46644$	$[0, 0, 0, -242427, -120140246]$	$y^2=x^3-242427x-120140246$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
114240.fc2	114240hg1	114240.fc	114240hg	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{28} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$1474560$	$2.076656$	$-527690404915129/1782829440000$	$0.95803$	$4.14721$	$[0, -1, 0, -107745, 35633025]$	$y^2=x^3-x^2-107745x+35633025$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
114240.iv2	114240ed1	114240.iv	114240ed	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{28} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$4.510775006$	$1$	$5$	$1474560$	$2.076656$	$-527690404915129/1782829440000$	$0.95803$	$4.14721$	$[0, 1, 0, -107745, -35633025]$	$y^2=x^3+x^2-107745x-35633025$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(450, 2685)]$
124950.ga2	124950fa1	124950.ga	124950fa	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7^{7} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1.069365245$	$1$	$9$	$8847360$	$2.814610$	$-527690404915129/1782829440000$	$0.95803$	$4.87012$	$[1, 1, 1, -2062313, 2980051031]$	$y^2+xy+y=x^3+x^2-2062313x+2980051031$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(615, 43792)]$
142800.s2	142800en1	142800.s	142800en	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{22} \cdot 3^{4} \cdot 5^{10} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1.325866796$	$1$	$7$	$4423680$	$2.534801$	$-527690404915129/1782829440000$	$0.95803$	$4.53244$	$[0, -1, 0, -673408, 556429312]$	$y^2=x^3-x^2-673408x+556429312$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(162, 21250)]$
182070.cw2	182070be1	182070.cw	182070be	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7 \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$17694720$	$3.002850$	$-527690404915129/1782829440000$	$0.95803$	$4.90524$	$[1, -1, 1, -4378838, 9223735781]$	$y^2+xy+y=x^3-x^2-4378838x+9223735781$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
199920.ct2	199920cg1	199920.ct	199920cg	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{22} \cdot 3^{4} \cdot 5^{4} \cdot 7^{7} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.685117253$	$1$	$11$	$8847360$	$2.703041$	$-527690404915129/1782829440000$	$0.95803$	$4.57290$	$[0, -1, 0, -1319880, -1525786128]$	$y^2=x^3-x^2-1319880x-1525786128$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(2154, 74970)]$
303450.dw2	303450dw1	303450.dw	303450dw	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} $	$ - 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7 \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$53084160$	$3.258263$	$-527690404915129/1782829440000$	$0.95803$	$4.94954$	$[1, 1, 1, -12163438, -42702480469]$	$y^2+xy+y=x^3+x^2-12163438x-42702480469$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
342720.cr2	342720cr1	342720.cr	342720cr	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{28} \cdot 3^{10} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1.701650904$	$1$	$5$	$11796480$	$2.625965$	$-527690404915129/1782829440000$	$0.95803$	$4.30693$	$[0, 0, 0, -969708, 961121968]$	$y^2=x^3-969708x+961121968$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-282, 34816)]$
342720.em2	342720em1	342720.em	342720em	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 $	$ - 2^{28} \cdot 3^{10} \cdot 5^{4} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$3.375087298$	$1$	$3$	$11796480$	$2.625965$	$-527690404915129/1782829440000$	$0.95803$	$4.30693$	$[0, 0, 0, -969708, -961121968]$	$y^2=x^3-969708x-961121968$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(2764, 132192)]$
374850.cz2	374850cz1	374850.cz	374850cz	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{10} \cdot 5^{10} \cdot 7^{7} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$70778880$	$3.363918$	$-527690404915129/1782829440000$	$0.95803$	$4.96684$	$[1, -1, 0, -18560817, -80479938659]$	$y^2+xy=x^3-x^2-18560817x-80479938659$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
424830.h2	424830h1	424830.h	424830h	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} $	$ - 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{7} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$	$1$	$106168320$	$3.426498$	$-527690404915129/1782829440000$	$0.95803$	$4.97682$	$[1, 1, 0, -23840338, 117151766068]$	$y^2+xy=x^3+x^2-23840338x+117151766068$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[]$
428400.ey2	428400ey1	428400.ey	428400ey	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 $	$ - 2^{22} \cdot 3^{10} \cdot 5^{10} \cdot 7 \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$11.66549624$	$1$	$3$	$35389440$	$3.084110$	$-527690404915129/1782829440000$	$0.95803$	$4.65677$	$[0, 0, 0, -6060675, -15017530750]$	$y^2=x^3-6060675x-15017530750$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(10481695, 33934954050)]$
431970.eg2	431970eg1	431970.eg	431970eg	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 $	$ - 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 11^{6} \cdot 17^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.819927373$	$1$	$9$	$10752000$	$2.235886$	$-527690404915129/1782829440000$	$0.95803$	$3.86937$	$[1, 1, 1, -203706, 92453703]$	$y^2+xy+y=x^3+x^2-203706x+92453703$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(301, 7499)]$
485520.cw2	485520cw1	485520.cw	485520cw	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} $	$ - 2^{22} \cdot 3^{4} \cdot 5^{4} \cdot 7 \cdot 17^{9} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.6.0.1	2B	$952$	$12$	$0$	$3.205545509$	$1$	$3$	$53084160$	$3.146690$	$-527690404915129/1782829440000$	$0.95803$	$4.66961$	$[0, -1, 0, -7784600, 21863670000]$	$y^2=x^3-x^2-7784600x+21863670000$	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(33785, 6190380)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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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