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 (24 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
9702.d1	9702g2	9702.d	9702g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{3} \cdot 7^{9} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$275968$	$2.458027$	$144106117295241933/247808$	$[1, -1, 0, -11239188, -14499945776]$	\(y^2+xy=x^3-x^2-11239188x-14499945776\)
9702.u1	9702e2	9702.u	9702e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$39424$	$1.485073$	$144106117295241933/247808$	$[1, -1, 0, -229371, 42339429]$	\(y^2+xy=x^3-x^2-229371x+42339429\)
9702.bh1	9702bl2	9702.bh	9702bl	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{9} \cdot 7^{3} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$118272$	$2.034378$	$144106117295241933/247808$	$[1, -1, 1, -2064341, -1141100243]$	\(y^2+xy+y=x^3-x^2-2064341x-1141100243\)
9702.cb1	9702bj2	9702.cb	9702bj	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{9} \cdot 7^{9} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$827904$	$3.007336$	$144106117295241933/247808$	$[1, -1, 1, -101152694, 391599688645]$	\(y^2+xy+y=x^3-x^2-101152694x+391599688645\)
77616.bj1	77616dj2	77616.bj	77616dj	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{23} \cdot 3^{9} \cdot 7^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.991876090$	$1$		$3$	$2838528$	$2.727528$	$144106117295241933/247808$	$[0, 0, 0, -33029451, 73063444986]$	\(y^2=x^3-33029451x+73063444986\)
77616.bt1	77616dx2	77616.bt	77616dx	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{23} \cdot 3^{3} \cdot 7^{9} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$6623232$	$3.151176$	$144106117295241933/247808$	$[0, 0, 0, -179827011, 928176356674]$	\(y^2=x^3-179827011x+928176356674\)
77616.fe1	77616dh2	77616.fe	77616dh	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{23} \cdot 3^{9} \cdot 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$42.29007542$	$1$		$1$	$19869696$	$3.700481$	$144106117295241933/247808$	$[0, 0, 0, -1618443099, -25060761630198]$	\(y^2=x^3-1618443099x-25060761630198\)
77616.fx1	77616du2	77616.fx	77616du	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{23} \cdot 3^{3} \cdot 7^{3} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$9$	$3$	$1$	$946176$	$2.178223$	$144106117295241933/247808$	$[0, 0, 0, -3669939, -2706053518]$	\(y^2=x^3-3669939x-2706053518\)
106722.w1	106722bd2	106722.w	106722bd	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{11} \cdot 3^{9} \cdot 7^{3} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.928584796$	$1$		$2$	$14192640$	$3.233326$	$144106117295241933/247808$	$[1, -1, 0, -249785223, 1519553778749]$	\(y^2+xy=x^3-x^2-249785223x+1519553778749\)
106722.de1	106722y2	106722.de	106722y	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{11} \cdot 3^{9} \cdot 7^{9} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$106.5325514$	$1$		$0$	$99348480$	$4.206284$	$144106117295241933/247808$	$[1, -1, 0, -12239475936, -521182467159040]$	\(y^2+xy=x^3-x^2-12239475936x-521182467159040\)
106722.fb1	106722fb2	106722.fb	106722fb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{11} \cdot 3^{3} \cdot 7^{9} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$33116160$	$3.656975$	$144106117295241933/247808$	$[1, -1, 1, -1359941771, 19303507653147]$	\(y^2+xy+y=x^3-x^2-1359941771x+19303507653147\)
106722.go1	106722ev2	106722.go	106722ev	$2$	$2$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{11} \cdot 3^{3} \cdot 7^{3} \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$0$	$4730880$	$2.684021$	$144106117295241933/247808$	$[1, -1, 1, -27753914, -56270518279]$	\(y^2+xy+y=x^3-x^2-27753914x-56270518279\)
242550.ff1	242550ff2	242550.ff	242550ff	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{9} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$26.45427057$	$1$		$0$	$15138816$	$2.839100$	$144106117295241933/247808$	$[1, -1, 0, -51608517, -142689138859]$	\(y^2+xy=x^3-x^2-51608517x-142689138859\)
242550.gi1	242550gi2	242550.gi	242550gi	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{9} \cdot 5^{6} \cdot 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$13.45358872$	$1$		$2$	$105971712$	$3.812054$	$144106117295241933/247808$	$[1, -1, 0, -2528817342, 48947432263316]$	\(y^2+xy=x^3-x^2-2528817342x+48947432263316\)
242550.iv1	242550iv2	242550.iv	242550iv	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.624829467$	$1$		$8$	$5046272$	$2.289791$	$144106117295241933/247808$	$[1, -1, 1, -5734280, 5286694347]$	\(y^2+xy+y=x^3-x^2-5734280x+5286694347\)
242550.kh1	242550kh2	242550.kh	242550kh	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{11} \cdot 3^{3} \cdot 5^{6} \cdot 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.173937777$	$1$		$2$	$35323904$	$3.262749$	$144106117295241933/247808$	$[1, -1, 1, -280979705, -1812774201703]$	\(y^2+xy+y=x^3-x^2-280979705x-1812774201703\)
310464.cu1	310464cu2	310464.cu	310464cu	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{3} \cdot 7^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$12.06824265$	$1$		$1$	$7569408$	$2.524796$	$144106117295241933/247808$	$[0, 0, 0, -14679756, -21648428144]$	\(y^2=x^3-14679756x-21648428144\)
310464.di1	310464di2	310464.di	310464di	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{9} \cdot 7^{9} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$9$	$3$	$1$	$158957568$	$4.047058$	$144106117295241933/247808$	$[0, 0, 0, -6473772396, 200486093041584]$	\(y^2=x^3-6473772396x+200486093041584\)
310464.em1	310464em2	310464.em	310464em	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{3} \cdot 7^{3} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.272557922$	$1$		$3$	$7569408$	$2.524796$	$144106117295241933/247808$	$[0, 0, 0, -14679756, 21648428144]$	\(y^2=x^3-14679756x+21648428144\)
310464.fb1	310464fb2	310464.fb	310464fb	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{9} \cdot 7^{9} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$25$	$5$	$1$	$158957568$	$4.047058$	$144106117295241933/247808$	$[0, 0, 0, -6473772396, -200486093041584]$	\(y^2=x^3-6473772396x-200486093041584\)
310464.mw1	310464mw2	310464.mw	310464mw	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{9} \cdot 7^{3} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$22708224$	$3.074100$	$144106117295241933/247808$	$[0, 0, 0, -132117804, -584507559888]$	\(y^2=x^3-132117804x-584507559888\)
310464.nl1	310464nl2	310464.nl	310464nl	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{3} \cdot 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$8.709117348$	$1$		$3$	$52985856$	$3.497749$	$144106117295241933/247808$	$[0, 0, 0, -719308044, 7425410853392]$	\(y^2=x^3-719308044x+7425410853392\)
310464.on1	310464on2	310464.on	310464on	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{9} \cdot 7^{3} \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$22708224$	$3.074100$	$144106117295241933/247808$	$[0, 0, 0, -132117804, 584507559888]$	\(y^2=x^3-132117804x+584507559888\)
310464.pd1	310464pd2	310464.pd	310464pd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 \)	\( 2^{29} \cdot 3^{3} \cdot 7^{9} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$41.54905307$	$1$		$1$	$52985856$	$3.497749$	$144106117295241933/247808$	$[0, 0, 0, -719308044, -7425410853392]$	\(y^2=x^3-719308044x-7425410853392\)