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 (21 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3990.bb5	3990bb4	3990.bb	3990bb	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{2} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 19 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.45	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$2$	$30720$	$1.533607$	$3342636501165359/751262567039460$	$1.01579$	$5.02981$	$[1, 0, 0, 3115, 1317285]$	$y^2+xy=x^3+3115x+1317285$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 48.48.0-48.h.1.15, 152.48.0.?, $\ldots$	$[]$
11970.c5	11970r4	11970.c	11970r	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{2} \cdot 3^{30} \cdot 5 \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.11	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$245760$	$2.082912$	$3342636501165359/751262567039460$	$1.01579$	$5.14332$	$[1, -1, 0, 28035, -35566695]$	$y^2+xy=x^3-x^2+28035x-35566695$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0-8.n.1.3, $\ldots$	$[]$
19950.o5	19950g4	19950.o	19950g	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{2} \cdot 3^{24} \cdot 5^{7} \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$737280$	$2.338326$	$3342636501165359/751262567039460$	$1.01579$	$5.18752$	$[1, 1, 0, 77875, 164660625]$	$y^2+xy=x^3+x^2+77875x+164660625$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 20.12.0-4.c.1.2, 40.24.0-8.n.1.1, $\ldots$	$[]$
27930.ci5	27930cg3	27930.ci	27930cg	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 $	$ - 2^{2} \cdot 3^{24} \cdot 5 \cdot 7^{7} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$1474560$	$2.506561$	$3342636501165359/751262567039460$	$1.01579$	$5.21422$	$[1, 1, 1, 152634, -451676121]$	$y^2+xy+y=x^3+x^2+152634x-451676121$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 28.12.0-4.c.1.2, 40.24.0-8.n.1.7, $\ldots$	$[]$
31920.ba5	31920bk3	31920.ba	31920bk	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.55	2B	$31920$	$192$	$1$	$11.72712135$	$4$	$2$	$1$	$737280$	$2.226753$	$3342636501165359/751262567039460$	$1.01579$	$4.82333$	$[0, -1, 0, 49840, -84306240]$	$y^2=x^3-x^2+49840x-84306240$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 48.48.0-48.h.1.31, 152.48.0.?, $\ldots$	$[(78193/12, 17500769/12)]$
59850.fe5	59850fh3	59850.fe	59850fh	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{2} \cdot 3^{30} \cdot 5^{7} \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$5898240$	$2.887630$	$3342636501165359/751262567039460$	$1.01579$	$5.26867$	$[1, -1, 1, 700870, -4445136003]$	$y^2+xy+y=x^3-x^2+700870x-4445136003$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0.h.1, 60.12.0-4.c.1.2, $\ldots$	$[]$
75810.x5	75810w3	75810.x	75810w	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19^{2} $	$ - 2^{2} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.94	2B	$31920$	$192$	$1$	$16.55061398$	$1$		$0$	$11059200$	$3.005825$	$3342636501165359/751262567039460$	$1.01579$	$5.28405$	$[1, 1, 0, 1124508, -9033008796]$	$y^2+xy=x^3+x^2+1124508x-9033008796$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.3, 48.48.0-48.h.1.8, 76.12.0.?, $\ldots$	$[(275039365/117, 4549201731946/117)]$
83790.bi5	83790cn3	83790.bi	83790cn	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 $	$ - 2^{2} \cdot 3^{30} \cdot 5 \cdot 7^{7} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$6.256739012$	$1$		$2$	$11796480$	$3.055866$	$3342636501165359/751262567039460$	$1.01579$	$5.29037$	$[1, -1, 0, 1373706, 12196628968]$	$y^2+xy=x^3-x^2+1373706x+12196628968$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0.h.1, 80.24.0.?, $\ldots$	$[(-621, 105685)]$
95760.cu5	95760ea3	95760.cu	95760ea	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{30} \cdot 5 \cdot 7 \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.11	2B	$31920$	$192$	$1$	$7.906970545$	$4$	$2$	$3$	$5898240$	$2.776058$	$3342636501165359/751262567039460$	$1.01579$	$4.93604$	$[0, 0, 0, 448557, 2275819922]$	$y^2=x^3+448557x+2275819922$	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.1.3, $\ldots$	$[(1502, 79612)]$
127680.d5	127680j3	127680.d	127680j	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{20} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.97	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$1$	$5898240$	$2.573326$	$3342636501165359/751262567039460$	$1.01579$	$4.60834$	$[0, -1, 0, 199359, 674250561]$	$y^2=x^3-x^2+199359x+674250561$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 48.48.0-48.h.1.27, 152.48.0.?, $\ldots$	$[]$
127680.ew5	127680fi3	127680.ew	127680fi	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{20} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.95	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$1$	$5898240$	$2.573326$	$3342636501165359/751262567039460$	$1.01579$	$4.60834$	$[0, 1, 0, 199359, -674250561]$	$y^2=x^3+x^2+199359x-674250561$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 48.48.0-48.h.1.11, 152.48.0.?, $\ldots$	$[]$
139650.ef5	139650ha4	139650.ef	139650ha	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{2} \cdot 3^{24} \cdot 5^{7} \cdot 7^{7} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.89	2B	$31920$	$192$	$1$	$1$	$1$		$0$	$35389440$	$3.311279$	$3342636501165359/751262567039460$	$1.01579$	$5.32097$	$[1, 0, 1, 3815849, -56467146802]$	$y^2+xy+y=x^3+3815849x-56467146802$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 48.48.0-48.h.1.9, 76.12.0.?, $\ldots$	$[]$
159600.do5	159600bt4	159600.do	159600bt	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{24} \cdot 5^{7} \cdot 7 \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$10.90968063$	$1$		$9$	$17694720$	$3.031471$	$3342636501165359/751262567039460$	$1.01579$	$4.98140$	$[0, 1, 0, 1245992, -10535788012]$	$y^2=x^3+x^2+1245992x-10535788012$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 20.12.0-4.c.1.1, 40.24.0-8.n.1.5, $\ldots$	$[(2732, 115182), (10103, 1016550)]$
223440.dt5	223440bv3	223440.dt	223440bv	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 $	$ - 2^{14} \cdot 3^{24} \cdot 5 \cdot 7^{7} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$8.340871073$	$1$		$11$	$35389440$	$3.199707$	$3342636501165359/751262567039460$	$1.01579$	$5.00923$	$[0, 1, 0, 2442144, 28912156020]$	$y^2=x^3+x^2+2442144x+28912156020$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 28.12.0-4.c.1.1, 40.24.0-8.n.1.3, $\ldots$	$[(1164, 182574), (-2364, 99666)]$
227430.dg5	227430bq3	227430.dg	227430bq	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19^{2} $	$ - 2^{2} \cdot 3^{30} \cdot 5 \cdot 7 \cdot 19^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.3	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$88473600$	$3.555134$	$3342636501165359/751262567039460$	$1.01579$	$5.34782$	$[1, -1, 1, 10120567, 243901358061]$	$y^2+xy+y=x^3-x^2+10120567x+243901358061$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 24.24.0-8.n.1.3, $\ldots$	$[]$
379050.kd5	379050kd4	379050.kd	379050kd	$6$	$8$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19^{2} $	$ - 2^{2} \cdot 3^{24} \cdot 5^{7} \cdot 7 \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$9.114803904$	$1$		$2$	$265420800$	$3.810547$	$3342636501165359/751262567039460$	$1.01579$	$5.37376$	$[1, 0, 0, 28112687, -1129182324883]$	$y^2+xy=x^3+28112687x-1129182324883$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 28.12.0-4.c.1.1, 40.24.0-8.n.1.3, $\ldots$	$[(475322, 327485189)]$
383040.ki5	383040ki4	383040.ki	383040ki	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{20} \cdot 3^{30} \cdot 5 \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.4	2B	$31920$	$192$	$1$	$1$	$16$	$2$	$1$	$47185920$	$3.122635$	$3342636501165359/751262567039460$	$1.01579$	$4.72727$	$[0, 0, 0, 1794228, -18206559376]$	$y^2=x^3+1794228x-18206559376$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.9, $\ldots$	$[]$
383040.lp5	383040lp3	383040.lp	383040lp	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 $	$ - 2^{20} \cdot 3^{30} \cdot 5 \cdot 7 \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.4	2B	$31920$	$192$	$1$	$8.216601817$	$4$	$2$	$3$	$47185920$	$3.122635$	$3342636501165359/751262567039460$	$1.01579$	$4.72727$	$[0, 0, 0, 1794228, 18206559376]$	$y^2=x^3+1794228x+18206559376$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.11, $\ldots$	$[(5340, 424336)]$
418950.ko5	418950ko3	418950.ko	418950ko	$6$	$8$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{2} \cdot 3^{30} \cdot 5^{7} \cdot 7^{7} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.24.0.3	2B	$31920$	$192$	$1$	$10.57509046$	$4$	$2$	$2$	$283115520$	$3.860588$	$3342636501165359/751262567039460$	$1.01579$	$5.37860$	$[1, -1, 1, 34342645, 1524612963647]$	$y^2+xy+y=x^3-x^2+34342645x+1524612963647$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 24.24.0-8.n.1.7, $\ldots$	$[(47323, 10422696)]$
478800.gk5	478800gk3	478800.gk	478800gk	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{14} \cdot 3^{30} \cdot 5^{7} \cdot 7 \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$1$	$141557760$	$3.580780$	$3342636501165359/751262567039460$	$1.01579$	$5.06696$	$[0, 0, 0, 11213925, 284477490250]$	$y^2=x^3+11213925x+284477490250$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0.h.1, 60.12.0-4.c.1.1, $\ldots$	$[]$
482790.dr5	482790dr4	482790.dr	482790dr	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 19 $	$ - 2^{2} \cdot 3^{24} \cdot 5 \cdot 7 \cdot 11^{6} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.12.0.5	2B	$351120$	$192$	$1$	$9.376272649$	$1$		$6$	$39321600$	$2.732555$	$3342636501165359/751262567039460$	$1.01579$	$4.28600$	$[1, 0, 1, 376912, -1752929422]$	$y^2+xy+y=x^3+376912x-1752929422$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 44.12.0-4.c.1.2, 48.24.0.h.1, $\ldots$	$[(2742, 139690), (1608, 54073)]$

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Classical	Maass
Hilbert	Bianchi

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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