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 (27 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
2310.b2	2310b2	2310.b	2310b	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$1$	$1$		$2$	$50176$	$2.171783$	$2436531580079063806249/1405478914998681600$	$[1, 1, 0, -280338, -3362508]$	\(y^2+xy=x^3+x^2-280338x-3362508\)
6930.bc2	6930be2	6930.bc	6930be	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{20} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$401408$	$2.721088$	$2436531580079063806249/1405478914998681600$	$[1, -1, 1, -2523047, 88264671]$	\(y^2+xy+y=x^3-x^2-2523047x+88264671\)
11550.cr2	11550cm2	11550.cr	11550cm	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$0.208557746$	$1$		$30$	$1204224$	$2.976501$	$2436531580079063806249/1405478914998681600$	$[1, 0, 0, -7008463, -406296583]$	\(y^2+xy=x^3-7008463x-406296583\)
16170.bc2	16170bh2	16170.bc	16170bh	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{14} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$0.933736480$	$1$		$14$	$2408448$	$3.144737$	$2436531580079063806249/1405478914998681600$	$[1, 0, 1, -13736588, 1112130506]$	\(y^2+xy+y=x^3-13736588x+1112130506\)
18480.cf2	18480cr2	18480.cf	18480cr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{26} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$1204224$	$2.864929$	$2436531580079063806249/1405478914998681600$	$[0, 1, 0, -4485416, 206229684]$	\(y^2=x^3+x^2-4485416x+206229684\)
25410.bo2	25410bx2	25410.bo	25410bx	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{14} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$6021120$	$3.370731$	$2436531580079063806249/1405478914998681600$	$[1, 1, 1, -33920961, 4305893439]$	\(y^2+xy+y=x^3+x^2-33920961x+4305893439\)
34650.ba2	34650bc2	34650.ba	34650bc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{14} \cdot 3^{20} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$8.061154608$	$1$		$2$	$9633792$	$3.525806$	$2436531580079063806249/1405478914998681600$	$[1, -1, 0, -63076167, 10970007741]$	\(y^2+xy=x^3-x^2-63076167x+10970007741\)
48510.cb2	48510dc2	48510.cb	48510dc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{20} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$19267584$	$3.694042$	$2436531580079063806249/1405478914998681600$	$[1, -1, 1, -123629288, -30027523669]$	\(y^2+xy+y=x^3-x^2-123629288x-30027523669\)
55440.ey2	55440ex2	55440.ey	55440ex	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{26} \cdot 3^{20} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$4$	$2$	$3$	$9633792$	$3.414234$	$2436531580079063806249/1405478914998681600$	$[0, 0, 0, -40368747, -5608570214]$	\(y^2=x^3-40368747x-5608570214\)
73920.dt2	73920gb2	73920.dt	73920gb	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$8.961982731$	$1$		$3$	$9633792$	$3.211502$	$2436531580079063806249/1405478914998681600$	$[0, -1, 0, -17941665, 1667779137]$	\(y^2=x^3-x^2-17941665x+1667779137\)
73920.gk2	73920df2	73920.gk	73920df	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3.370520506$	$1$		$9$	$9633792$	$3.211502$	$2436531580079063806249/1405478914998681600$	$[0, 1, 0, -17941665, -1667779137]$	\(y^2=x^3+x^2-17941665x-1667779137\)
76230.cb2	76230cq2	76230.cb	76230cq	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{14} \cdot 3^{20} \cdot 5^{2} \cdot 7^{2} \cdot 11^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15.29721683$	$1$		$2$	$48168960$	$3.920036$	$2436531580079063806249/1405478914998681600$	$[1, -1, 0, -305288649, -116564411507]$	\(y^2+xy=x^3-x^2-305288649x-116564411507\)
80850.fj2	80850et2	80850.fj	80850et	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{14} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$57802752$	$3.949455$	$2436531580079063806249/1405478914998681600$	$[1, 1, 1, -343414688, 139016313281]$	\(y^2+xy+y=x^3+x^2-343414688x+139016313281\)
92400.b2	92400dn2	92400.b	92400dn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{26} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$28901376$	$3.669647$	$2436531580079063806249/1405478914998681600$	$[0, -1, 0, -112135408, 26002981312]$	\(y^2=x^3-x^2-112135408x+26002981312\)
127050.do2	127050dd2	127050.do	127050dd	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{14} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.849123182$	$1$		$4$	$144506880$	$4.175446$	$2436531580079063806249/1405478914998681600$	$[1, 0, 1, -848024026, 539932727948]$	\(y^2+xy+y=x^3-848024026x+539932727948\)
129360.cj2	129360ff2	129360.cj	129360ff	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{26} \cdot 3^{14} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$57802752$	$3.837883$	$2436531580079063806249/1405478914998681600$	$[0, -1, 0, -219785400, -71176352400]$	\(y^2=x^3-x^2-219785400x-71176352400\)
177870.jc2	177870bc2	177870.jc	177870bc	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( 2^{14} \cdot 3^{14} \cdot 5^{2} \cdot 7^{8} \cdot 11^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$289013760$	$4.343689$	$2436531580079063806249/1405478914998681600$	$[1, 0, 0, -1662127090, -1481907830908]$	\(y^2+xy=x^3-1662127090x-1481907830908\)
203280.dt2	203280br2	203280.dt	203280br	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( 2^{26} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$144506880$	$4.063881$	$2436531580079063806249/1405478914998681600$	$[0, 1, 0, -542735376, -276662650860]$	\(y^2=x^3+x^2-542735376x-276662650860\)
221760.bu2	221760lj2	221760.bu	221760lj	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{20} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$5.396667190$	$1$		$5$	$77070336$	$3.760811$	$2436531580079063806249/1405478914998681600$	$[0, 0, 0, -161474988, 44868561712]$	\(y^2=x^3-161474988x+44868561712\)
221760.di2	221760dq2	221760.di	221760dq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{20} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$77070336$	$3.760811$	$2436531580079063806249/1405478914998681600$	$[0, 0, 0, -161474988, -44868561712]$	\(y^2=x^3-161474988x-44868561712\)
242550.dp2	242550dp2	242550.dp	242550dp	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{14} \cdot 3^{20} \cdot 5^{8} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.2	2Cs	$16.92587364$	$1$		$2$	$462422016$	$4.498764$	$2436531580079063806249/1405478914998681600$	$[1, -1, 0, -3090732192, -3756531190784]$	\(y^2+xy=x^3-x^2-3090732192x-3756531190784\)
277200.dv2	277200dv2	277200.dv	277200dv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{26} \cdot 3^{20} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$231211008$	$4.218956$	$2436531580079063806249/1405478914998681600$	$[0, 0, 0, -1009218675, -701071276750]$	\(y^2=x^3-1009218675x-701071276750\)
369600.iz2	369600iz2	369600.iz	369600iz	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$9$	$3$	$3$	$231211008$	$4.016220$	$2436531580079063806249/1405478914998681600$	$[0, -1, 0, -448541633, -207575308863]$	\(y^2=x^3-x^2-448541633x-207575308863\)
369600.qr2	369600qr2	369600.qr	369600qr	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( 2^{32} \cdot 3^{14} \cdot 5^{8} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$231211008$	$4.016220$	$2436531580079063806249/1405478914998681600$	$[0, 1, 0, -448541633, 207575308863]$	\(y^2=x^3+x^2-448541633x+207575308863\)
381150.ms2	381150ms2	381150.ms	381150ms	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( 2^{14} \cdot 3^{20} \cdot 5^{8} \cdot 7^{2} \cdot 11^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$1156055040$	$4.724754$	$2436531580079063806249/1405478914998681600$	$[1, -1, 1, -7632216230, -14578183654603]$	\(y^2+xy+y=x^3-x^2-7632216230x-14578183654603\)
388080.ei2	388080ei2	388080.ei	388080ei	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( 2^{26} \cdot 3^{20} \cdot 5^{2} \cdot 7^{8} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$8.300385675$	$1$		$5$	$462422016$	$4.387192$	$2436531580079063806249/1405478914998681600$	$[0, 0, 0, -1978068603, 1923739583402]$	\(y^2=x^3-1978068603x+1923739583402\)
390390.do2	390390do2	390390.do	390390do	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( 2^{14} \cdot 3^{14} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \cdot 13^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$96337920$	$3.454258$	$2436531580079063806249/1405478914998681600$	$[1, 1, 1, -47377210, -7150544185]$	\(y^2+xy+y=x^3+x^2-47377210x-7150544185\)