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 (29 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
966.g2	966g4	966.g	966g	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.159	2B	$2.429046614$	$1$		$12$	$2048$	$1.069401$	$614716917569296417/19093020912$	$[1, 1, 1, -17714, 900047]$	\(y^2+xy+y=x^3+x^2-17714x+900047\)
2898.i2	2898i3	2898.i	2898i	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$1$		$0$	$16384$	$1.618708$	$614716917569296417/19093020912$	$[1, -1, 0, -159426, -24460700]$	\(y^2+xy=x^3-x^2-159426x-24460700\)
6762.bl2	6762bh3	6762.bl	6762bh	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.98	2B	$1$	$4$	$2$	$0$	$98304$	$2.042355$	$614716917569296417/19093020912$	$[1, 0, 0, -867987, -311320143]$	\(y^2+xy=x^3-867987x-311320143\)
7728.o2	7728r3	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.176	2B	$1$	$4$	$2$	$1$	$49152$	$1.762548$	$614716917569296417/19093020912$	$[0, 1, 0, -283424, -58169868]$	\(y^2=x^3+x^2-283424x-58169868\)
20286.k2	20286be4	20286.k	20286be	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 7^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$1$		$0$	$786432$	$2.591663$	$614716917569296417/19093020912$	$[1, -1, 0, -7811883, 8405643861]$	\(y^2+xy=x^3-x^2-7811883x+8405643861\)
22218.y2	22218t4	22218.y	22218t	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 23^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.182	2B	$11.55242510$	$1$		$0$	$1081344$	$2.637150$	$614716917569296417/19093020912$	$[1, 1, 1, -9370717, -11044581181]$	\(y^2+xy+y=x^3+x^2-9370717x-11044581181\)
23184.bk2	23184bi4	23184.bk	23184bi	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{8} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$8.479681894$	$1$		$3$	$393216$	$2.311855$	$614716917569296417/19093020912$	$[0, 0, 0, -2550819, 1568035618]$	\(y^2=x^3-2550819x+1568035618\)
24150.y2	24150bc4	24150.y	24150bc	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$2.253624891$	$1$		$4$	$262144$	$1.874121$	$614716917569296417/19093020912$	$[1, 0, 1, -442851, 113391598]$	\(y^2+xy+y=x^3-442851x+113391598\)
30912.w2	30912bk4	30912.w	30912bk	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{22} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.215	2B	$16.50392216$	$1$		$1$	$393216$	$2.109123$	$614716917569296417/19093020912$	$[0, -1, 0, -1133697, -464225247]$	\(y^2=x^3-x^2-1133697x-464225247\)
30912.ci2	30912y4	30912.ci	30912y	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{22} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.219	2B	$1.330662386$	$1$		$3$	$393216$	$2.109123$	$614716917569296417/19093020912$	$[0, 1, 0, -1133697, 464225247]$	\(y^2=x^3+x^2-1133697x+464225247\)
54096.bi2	54096bw4	54096.bi	54096bw	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{16} \cdot 3^{2} \cdot 7^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.100	2B	$1$	$4$	$2$	$1$	$2359296$	$2.735504$	$614716917569296417/19093020912$	$[0, -1, 0, -13887792, 19924489152]$	\(y^2=x^3-x^2-13887792x+19924489152\)
66654.h2	66654j4	66654.h	66654j	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 7^{8} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1.753970187$	$1$		$6$	$8650752$	$3.186455$	$614716917569296417/19093020912$	$[1, -1, 0, -84336453, 298119355429]$	\(y^2+xy=x^3-x^2-84336453x+298119355429\)
72450.dp2	72450dn4	72450.dp	72450dn	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 5^{6} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$3.083374448$	$4$	$2$	$4$	$2097152$	$2.423428$	$614716917569296417/19093020912$	$[1, -1, 1, -3985655, -3061573153]$	\(y^2+xy+y=x^3-x^2-3985655x-3061573153\)
92736.bh2	92736dz4	92736.bh	92736dz	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{22} \cdot 3^{8} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$14.33007829$	$1$		$1$	$3145728$	$2.658428$	$614716917569296417/19093020912$	$[0, 0, 0, -10203276, 12544284944]$	\(y^2=x^3-10203276x+12544284944\)
92736.bk2	92736co4	92736.bk	92736co	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{22} \cdot 3^{8} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$1$		$1$	$3145728$	$2.658428$	$614716917569296417/19093020912$	$[0, 0, 0, -10203276, -12544284944]$	\(y^2=x^3-10203276x-12544284944\)
116886.c2	116886b4	116886.c	116886b	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 11^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$1$		$0$	$2621440$	$2.268349$	$614716917569296417/19093020912$	$[1, 1, 0, -2143396, -1208679776]$	\(y^2+xy=x^3+x^2-2143396x-1208679776\)
155526.cp2	155526h3	155526.cp	155526h	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 7^{14} \cdot 23^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.99	2B	$9.462297832$	$1$		$0$	$51904512$	$3.610104$	$614716917569296417/19093020912$	$[1, 0, 0, -459165134, 3786913849620]$	\(y^2+xy=x^3-459165134x+3786913849620\)
162288.bg2	162288o4	162288.bg	162288o	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{16} \cdot 3^{8} \cdot 7^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$4$	$2$	$1$	$18874368$	$3.284809$	$614716917569296417/19093020912$	$[0, 0, 0, -124990131, -537836216974]$	\(y^2=x^3-124990131x-537836216974\)
163254.u2	163254du3	163254.u	163254du	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 13^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1.892244855$	$1$		$6$	$4718592$	$2.351875$	$614716917569296417/19093020912$	$[1, 1, 0, -2993669, 1992371997]$	\(y^2+xy=x^3+x^2-2993669x+1992371997\)
169050.e2	169050ia4	169050.e	169050ia	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 7^{14} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4.451049067$	$1$		$4$	$12582912$	$2.847076$	$614716917569296417/19093020912$	$[1, 1, 0, -21699675, -38915017875]$	\(y^2+xy=x^3+x^2-21699675x-38915017875\)
177744.dd2	177744x3	177744.dd	177744x	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23^{2} \)	\( 2^{16} \cdot 3^{2} \cdot 7^{8} \cdot 23^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.165	2B	$12.14006495$	$1$		$3$	$25952256$	$3.330296$	$614716917569296417/19093020912$	$[0, 1, 0, -149931472, 706553332628]$	\(y^2=x^3+x^2-149931472x+706553332628\)
193200.df2	193200ef4	193200.df	193200ef	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{6} \cdot 7^{8} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$5.074500770$	$1$		$3$	$6291456$	$2.567268$	$614716917569296417/19093020912$	$[0, -1, 0, -7085608, -7257062288]$	\(y^2=x^3-x^2-7085608x-7257062288\)
216384.bd2	216384hm4	216384.bd	216384hm	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{22} \cdot 3^{2} \cdot 7^{14} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.104	2B	$1$	$4$	$2$	$1$	$18874368$	$3.082077$	$614716917569296417/19093020912$	$[0, -1, 0, -55551169, -159340362047]$	\(y^2=x^3-x^2-55551169x-159340362047\)
216384.fi2	216384l3	216384.fi	216384l	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{22} \cdot 3^{2} \cdot 7^{14} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.106	2B	$9.656910616$	$1$		$1$	$18874368$	$3.082077$	$614716917569296417/19093020912$	$[0, 1, 0, -55551169, 159340362047]$	\(y^2=x^3+x^2-55551169x+159340362047\)
279174.cr2	279174cr3	279174.cr	279174cr	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 17^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 17^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$4$	$2$	$0$	$9437184$	$2.486008$	$614716917569296417/19093020912$	$[1, 0, 0, -5119352, 4457767248]$	\(y^2+xy=x^3-5119352x+4457767248\)
348726.r2	348726r4	348726.r	348726r	$6$	$8$	\( 2 \cdot 3 \cdot 7 \cdot 19^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 7^{8} \cdot 19^{6} \cdot 23 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$3.972114551$	$1$		$10$	$14155776$	$2.541622$	$614716917569296417/19093020912$	$[1, 0, 1, -6394762, -6224581684]$	\(y^2+xy+y=x^3-6394762x-6224581684\)
350658.dw2	350658dw3	350658.dw	350658dw	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 7^{8} \cdot 11^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4.355893420$	$1$		$2$	$20971520$	$2.817654$	$614716917569296417/19093020912$	$[1, -1, 1, -19290569, 32615063385]$	\(y^2+xy+y=x^3-x^2-19290569x+32615063385\)
466578.ce2	466578ce4	466578.ce	466578ce	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 7^{14} \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1$	$9$	$3$	$0$	$415236096$	$4.159409$	$614716917569296417/19093020912$	$[1, -1, 0, -4132486206, -102246673939740]$	\(y^2+xy=x^3-x^2-4132486206x-102246673939740\)
489762.dg2	489762dg4	489762.dg	489762dg	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 \)	\( 2^{4} \cdot 3^{8} \cdot 7^{8} \cdot 13^{6} \cdot 23 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$20.02557843$	$1$		$6$	$37748736$	$2.901180$	$614716917569296417/19093020912$	$[1, -1, 1, -26943026, -53820986943]$	\(y^2+xy+y=x^3-x^2-26943026x-53820986943\)