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.b4	2310b4	2310.b	2310b	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$1$	$1$		$0$	$100352$	$2.518356$	$155099895405729262880471/90047655797243760000$	$[1, 1, 0, 1119342, -25477452]$	\(y^2+xy=x^3+x^2+1119342x-25477452\)
6930.bc4	6930be4	6930.bc	6930be	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$1$		$0$	$802816$	$3.067661$	$155099895405729262880471/90047655797243760000$	$[1, -1, 1, 10074073, 697965279]$	\(y^2+xy+y=x^3-x^2+10074073x+697965279\)
11550.cr4	11550cm4	11550.cr	11550cm	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$0.104278873$	$1$		$22$	$2408448$	$3.323074$	$155099895405729262880471/90047655797243760000$	$[1, 0, 0, 27983537, -3240648583]$	\(y^2+xy=x^3+27983537x-3240648583\)
16170.bc4	16170bh4	16170.bc	16170bh	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{4} \cdot 7^{10} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$0.466868240$	$1$		$8$	$4816896$	$3.491310$	$155099895405729262880471/90047655797243760000$	$[1, 0, 1, 54847732, 8903309258]$	\(y^2+xy+y=x^3+54847732x+8903309258\)
18480.cf4	18480cr4	18480.cf	18480cr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1$	$1$		$1$	$2408448$	$3.211502$	$155099895405729262880471/90047655797243760000$	$[0, 1, 0, 17909464, 1666375860]$	\(y^2=x^3+x^2+17909464x+1666375860\)
25410.bo4	25410bx3	25410.bo	25410bx	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$12042240$	$3.717304$	$155099895405729262880471/90047655797243760000$	$[1, 1, 1, 135440319, 34587690303]$	\(y^2+xy+y=x^3+x^2+135440319x+34587690303\)
34650.ba4	34650bc3	34650.ba	34650bc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.030577304$	$1$		$2$	$19267584$	$3.872383$	$155099895405729262880471/90047655797243760000$	$[1, -1, 0, 251851833, 87497511741]$	\(y^2+xy=x^3-x^2+251851833x+87497511741\)
48510.cb4	48510dc3	48510.cb	48510dc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{4} \cdot 7^{10} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$38535168$	$4.040619$	$155099895405729262880471/90047655797243760000$	$[1, -1, 1, 493629592, -240389349973]$	\(y^2+xy+y=x^3-x^2+493629592x-240389349973\)
55440.ey4	55440ex3	55440.ey	55440ex	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{19} \cdot 3^{13} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1$	$1$		$3$	$19267584$	$3.760811$	$155099895405729262880471/90047655797243760000$	$[0, 0, 0, 161185173, -44830963046]$	\(y^2=x^3+161185173x-44830963046\)
73920.dt4	73920gb3	73920.dt	73920gb	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$4.480991365$	$1$		$7$	$19267584$	$3.558079$	$155099895405729262880471/90047655797243760000$	$[0, -1, 0, 71637855, 13259369025]$	\(y^2=x^3-x^2+71637855x+13259369025\)
73920.gk4	73920df3	73920.gk	73920df	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1.685260253$	$1$		$7$	$19267584$	$3.558079$	$155099895405729262880471/90047655797243760000$	$[0, 1, 0, 71637855, -13259369025]$	\(y^2=x^3+x^2+71637855x-13259369025\)
76230.cb4	76230cq3	76230.cb	76230cq	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{4} \cdot 7^{4} \cdot 11^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7.648608419$	$1$		$0$	$96337920$	$4.266609$	$155099895405729262880471/90047655797243760000$	$[1, -1, 0, 1218962871, -932648675315]$	\(y^2+xy=x^3-x^2+1218962871x-932648675315\)
80850.fj4	80850et3	80850.fj	80850et	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{10} \cdot 7^{10} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1$	$1$		$0$	$115605504$	$4.296028$	$155099895405729262880471/90047655797243760000$	$[1, 1, 1, 1371193312, 1112913657281]$	\(y^2+xy+y=x^3+x^2+1371193312x+1112913657281\)
92400.b4	92400dn3	92400.b	92400dn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$57802752$	$4.016220$	$155099895405729262880471/90047655797243760000$	$[0, -1, 0, 447736592, 207401509312]$	\(y^2=x^3-x^2+447736592x+207401509312\)
127050.do4	127050dd3	127050.do	127050dd	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{10} \cdot 7^{4} \cdot 11^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7.698246364$	$1$		$0$	$289013760$	$4.522026$	$155099895405729262880471/90047655797243760000$	$[1, 0, 1, 3386007974, 4316689271948]$	\(y^2+xy+y=x^3+3386007974x+4316689271948\)
129360.cj4	129360ff3	129360.cj	129360ff	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{4} \cdot 7^{10} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$115605504$	$4.184456$	$155099895405729262880471/90047655797243760000$	$[0, -1, 0, 877563720, -569811792528]$	\(y^2=x^3-x^2+877563720x-569811792528\)
177870.jc4	177870bc4	177870.jc	177870bc	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{4} \cdot 7^{10} \cdot 11^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$578027520$	$4.690262$	$155099895405729262880471/90047655797243760000$	$[1, 0, 0, 6636575630, -11843668047100]$	\(y^2+xy=x^3+6636575630x-11843668047100\)
203280.dt4	203280br4	203280.dt	203280br	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$289013760$	$4.410454$	$155099895405729262880471/90047655797243760000$	$[0, 1, 0, 2167045104, -2209278089196]$	\(y^2=x^3+x^2+2167045104x-2209278089196\)
221760.bu4	221760lj3	221760.bu	221760lj	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{13} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$2.698333595$	$1$		$5$	$154140672$	$4.107384$	$155099895405729262880471/90047655797243760000$	$[0, 0, 0, 644740692, 358647704368]$	\(y^2=x^3+644740692x+358647704368\)
221760.di4	221760dq4	221760.di	221760dq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{13} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1$	$1$		$1$	$154140672$	$4.107384$	$155099895405729262880471/90047655797243760000$	$[0, 0, 0, 644740692, -358647704368]$	\(y^2=x^3+644740692x-358647704368\)
242550.dp4	242550dp4	242550.dp	242550dp	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{10} \cdot 7^{10} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$33.85174728$	$1$		$0$	$924844032$	$4.845337$	$155099895405729262880471/90047655797243760000$	$[1, -1, 0, 12340739808, -30036328006784]$	\(y^2+xy=x^3-x^2+12340739808x-30036328006784\)
277200.dv4	277200dv4	277200.dv	277200dv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{19} \cdot 3^{13} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$462422016$	$4.565529$	$155099895405729262880471/90047655797243760000$	$[0, 0, 0, 4029629325, -5603870380750]$	\(y^2=x^3+4029629325x-5603870380750\)
369600.iz4	369600iz4	369600.iz	369600iz	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{7} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$9$	$3$	$1$	$462422016$	$4.362793$	$155099895405729262880471/90047655797243760000$	$[0, -1, 0, 1790946367, -1661003020863]$	\(y^2=x^3-x^2+1790946367x-1661003020863\)
369600.qr4	369600qr3	369600.qr	369600qr	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{25} \cdot 3^{7} \cdot 5^{10} \cdot 7^{4} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$462422016$	$4.362793$	$155099895405729262880471/90047655797243760000$	$[0, 1, 0, 1790946367, 1661003020863]$	\(y^2=x^3+x^2+1790946367x+1661003020863\)
381150.ms4	381150ms4	381150.ms	381150ms	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{7} \cdot 3^{13} \cdot 5^{10} \cdot 7^{4} \cdot 11^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$2312110080$	$5.071327$	$155099895405729262880471/90047655797243760000$	$[1, -1, 1, 30474071770, -116550610342603]$	\(y^2+xy+y=x^3-x^2+30474071770x-116550610342603\)
388080.ei4	388080ei3	388080.ei	388080ei	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{19} \cdot 3^{13} \cdot 5^{4} \cdot 7^{10} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.150192837$	$1$		$5$	$924844032$	$4.733765$	$155099895405729262880471/90047655797243760000$	$[0, 0, 0, 7898073477, 15377020324778]$	\(y^2=x^3+7898073477x+15377020324778\)
390390.do4	390390do4	390390.do	390390do	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{4} \cdot 7^{4} \cdot 11^{8} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$0$	$192675840$	$3.800831$	$155099895405729262880471/90047655797243760000$	$[1, 1, 1, 189168710, -56919805753]$	\(y^2+xy+y=x^3+x^2+189168710x-56919805753\)