Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (31 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
1155.k3	1155f1	1155.k	1155f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$4.472209988$	$1$		$3$	$1152$	$0.822330$	$473897054735271721/779625$	$[1, 1, 0, -16242, -803529]$	\(y^2+xy=x^3+x^2-16242x-803529\)
3465.b3	3465k1	3465.b	3465k	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{10} \cdot 5^{3} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$9216$	$1.371635$	$473897054735271721/779625$	$[1, -1, 1, -146183, 21549102]$	\(y^2+xy+y=x^3-x^2-146183x+21549102\)
5775.g3	5775o1	5775.g	5775o	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{9} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$27648$	$1.627048$	$473897054735271721/779625$	$[1, 0, 0, -406063, -99629008]$	\(y^2+xy=x^3-406063x-99629008\)
8085.u3	8085n1	8085.u	8085n	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 3^{4} \cdot 5^{3} \cdot 7^{7} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.111801264$	$1$		$3$	$55296$	$1.795284$	$473897054735271721/779625$	$[1, 0, 1, -795884, 273222821]$	\(y^2+xy+y=x^3-795884x+273222821\)
12705.c3	12705e1	12705.c	12705e	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3.114754950$	$1$		$9$	$138240$	$2.021278$	$473897054735271721/779625$	$[1, 1, 1, -1965345, 1059670470]$	\(y^2+xy+y=x^3+x^2-1965345x+1059670470\)
17325.bi3	17325q1	17325.bi	17325q	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 3^{10} \cdot 5^{9} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2.926043898$	$1$		$1$	$221184$	$2.176353$	$473897054735271721/779625$	$[1, -1, 0, -3654567, 2689983216]$	\(y^2+xy=x^3-x^2-3654567x+2689983216\)
18480.cq3	18480dc1	18480.cq	18480dc	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$0.566806575$	$1$		$9$	$73728$	$1.515476$	$473897054735271721/779625$	$[0, 1, 0, -259880, 50906100]$	\(y^2=x^3+x^2-259880x+50906100\)
24255.o3	24255bu1	24255.o	24255bu	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 3^{10} \cdot 5^{3} \cdot 7^{7} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6.296632121$	$1$		$3$	$442368$	$2.344589$	$473897054735271721/779625$	$[1, -1, 1, -7162952, -7377016174]$	\(y^2+xy+y=x^3-x^2-7162952x-7377016174\)
38115.u3	38115j1	38115.u	38115j	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 3^{10} \cdot 5^{3} \cdot 7 \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$34.99995006$	$1$		$1$	$1105920$	$2.570583$	$473897054735271721/779625$	$[1, -1, 0, -17688105, -28628790800]$	\(y^2+xy=x^3-x^2-17688105x-28628790800\)
40425.i3	40425m1	40425.i	40425m	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 3^{4} \cdot 5^{9} \cdot 7^{7} \cdot 11 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1$	$1$		$3$	$1327104$	$2.600002$	$473897054735271721/779625$	$[1, 1, 1, -19897088, 34152852656]$	\(y^2+xy+y=x^3+x^2-19897088x+34152852656\)
55440.l3	55440cv1	55440.l	55440cv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10.27159475$	$1$		$1$	$589824$	$2.064781$	$473897054735271721/779625$	$[0, 0, 0, -2338923, -1376803622]$	\(y^2=x^3-2338923x-1376803622\)
63525.ce3	63525bs1	63525.ce	63525bs	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 3^{4} \cdot 5^{9} \cdot 7 \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$3317760$	$2.825996$	$473897054735271721/779625$	$[1, 0, 1, -49133626, 132557076023]$	\(y^2+xy+y=x^3-49133626x+132557076023\)
73920.l3	73920ec1	73920.l	73920ec	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$1$		$1$	$589824$	$1.862051$	$473897054735271721/779625$	$[0, -1, 0, -1039521, 408288321]$	\(y^2=x^3-x^2-1039521x+408288321\)
73920.gc3	73920cx1	73920.gc	73920cx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$4$	$2$	$1$	$589824$	$1.862051$	$473897054735271721/779625$	$[0, 1, 0, -1039521, -408288321]$	\(y^2=x^3+x^2-1039521x-408288321\)
88935.s3	88935br1	88935.s	88935br	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( 3^{4} \cdot 5^{3} \cdot 7^{7} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$6635520$	$2.994232$	$473897054735271721/779625$	$[1, 0, 0, -96301906, -363755876989]$	\(y^2+xy=x^3-96301906x-363755876989\)
92400.dv3	92400em1	92400.dv	92400em	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{9} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$1769472$	$2.320194$	$473897054735271721/779625$	$[0, -1, 0, -6497008, 6376256512]$	\(y^2=x^3-x^2-6497008x+6376256512\)
121275.fg3	121275ed1	121275.fg	121275ed	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 3^{10} \cdot 5^{9} \cdot 7^{7} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$9$	$3$	$1$	$10616832$	$3.149311$	$473897054735271721/779625$	$[1, -1, 0, -179073792, -922306095509]$	\(y^2+xy=x^3-x^2-179073792x-922306095509\)
129360.cc3	129360eh1	129360.cc	129360eh	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{3} \cdot 7^{7} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$3538944$	$2.488430$	$473897054735271721/779625$	$[0, -1, 0, -12734136, -17486260560]$	\(y^2=x^3-x^2-12734136x-17486260560\)
190575.bu3	190575bg1	190575.bu	190575bg	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 3^{10} \cdot 5^{9} \cdot 7 \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$26542080$	$3.375301$	$473897054735271721/779625$	$[1, -1, 1, -442202630, -3579041052628]$	\(y^2+xy+y=x^3-x^2-442202630x-3579041052628\)
195195.d3	195195p1	195195.d	195195p	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$2654208$	$2.104805$	$473897054735271721/779625$	$[1, 1, 1, -2744986, -1751628442]$	\(y^2+xy+y=x^3+x^2-2744986x-1751628442\)
203280.hi3	203280n1	203280.hi	203280n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{12} \cdot 3^{4} \cdot 5^{3} \cdot 7 \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$4$	$2$	$1$	$8847360$	$2.714424$	$473897054735271721/779625$	$[0, 1, 0, -31445520, -67881801132]$	\(y^2=x^3+x^2-31445520x-67881801132\)
221760.jt3	221760ce1	221760.jt	221760ce	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{10} \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9.090849873$	$1$		$1$	$4718592$	$2.411358$	$473897054735271721/779625$	$[0, 0, 0, -9355692, -11014428976]$	\(y^2=x^3-9355692x-11014428976\)
221760.ma3	221760iv1	221760.ma	221760iv	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{10} \cdot 5^{3} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$4718592$	$2.411358$	$473897054735271721/779625$	$[0, 0, 0, -9355692, 11014428976]$	\(y^2=x^3-9355692x+11014428976\)
266805.dv3	266805dv1	266805.dv	266805dv	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( 3^{10} \cdot 5^{3} \cdot 7^{7} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3.888007976$	$1$		$1$	$53084160$	$3.543537$	$473897054735271721/779625$	$[1, -1, 0, -866717154, 9821408678703]$	\(y^2+xy=x^3-x^2-866717154x+9821408678703\)
277200.jm3	277200jm1	277200.jm	277200jm	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{9} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$14155776$	$2.869503$	$473897054735271721/779625$	$[0, 0, 0, -58473075, -172100452750]$	\(y^2=x^3-58473075x-172100452750\)
333795.bt3	333795bt1	333795.bt	333795bt	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \cdot 17^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$12.63566525$	$4$	$2$	$1$	$5308416$	$2.238937$	$473897054735271721/779625$	$[1, 0, 1, -4694089, -3914879713]$	\(y^2+xy+y=x^3-4694089x-3914879713\)
369600.eg3	369600eg1	369600.eg	369600eg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{9} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$14155776$	$2.666771$	$473897054735271721/779625$	$[0, -1, 0, -25988033, -50984064063]$	\(y^2=x^3-x^2-25988033x-50984064063\)
369600.sb3	369600sb1	369600.sb	369600sb	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{9} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$14155776$	$2.666771$	$473897054735271721/779625$	$[0, 1, 0, -25988033, 50984064063]$	\(y^2=x^3+x^2-25988033x+50984064063\)
388080.ka3	388080ka1	388080.ka	388080ka	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{3} \cdot 7^{7} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$0.897991065$	$1$		$9$	$28311552$	$3.037739$	$473897054735271721/779625$	$[0, 0, 0, -114607227, 472243642346]$	\(y^2=x^3-114607227x+472243642346\)
416955.ba3	416955ba1	416955.ba	416955ba	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \cdot 19^{2} \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.327949587$	$1$		$5$	$7962624$	$2.294548$	$473897054735271721/779625$	$[1, 0, 0, -5863550, 5464497507]$	\(y^2+xy=x^3-5863550x+5464497507\)
444675.fx3	444675fx1	444675.fx	444675fx	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 3^{4} \cdot 5^{9} \cdot 7^{7} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$27.30776175$	$1$		$1$	$159252480$	$3.798950$	$473897054735271721/779625$	$[1, 1, 0, -2407547650, -45469484623625]$	\(y^2+xy=x^3+x^2-2407547650x-45469484623625\)