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 (20 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
54.b2	54b3	54.b	54b	$3$	$9$	\( 2 \cdot 3^{3} \)	\( - 2^{9} \cdot 3^{5} \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$6$	$-0.315205$	$-1167051/512$	$[1, -1, 1, -14, 29]$	\(y^2+xy+y=x^3-x^2-14x+29\)
714.i3	714i1	714.i	714i	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 17 \)	\( - 2^{9} \cdot 3^{9} \cdot 7^{3} \cdot 17 \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$1080$	$0.745499$	$139233463487/58763045376$	$[1, 0, 0, 108, 11664]$	\(y^2+xy=x^3+108x+11664\)
1482.j3	1482l1	1482.j	1482l	$3$	$9$	\( 2 \cdot 3 \cdot 13 \cdot 19 \)	\( - 2^{18} \cdot 3^{9} \cdot 13^{3} \cdot 19 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1.735730763$	$1$		$24$	$7776$	$1.437672$	$240065464752030527/215384711233536$	$[1, 0, 0, 12948, 421776]$	\(y^2+xy=x^3+12948x+421776\)
1554.l2	1554n1	1554.l	1554n	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 37 \)	\( - 2^{9} \cdot 3^{9} \cdot 7^{3} \cdot 37 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1.255479514$	$1$		$24$	$3888$	$0.947635$	$-11980221891814513/127896039936$	$[1, 0, 0, -4767, 127449]$	\(y^2+xy=x^3-4767x+127449\)
1890.x3	1890r3	1890.x	1890r	$3$	$9$	\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{9} \cdot 7^{3} \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$19440$	$1.876335$	$114115456478544693/175616000000000$	$[1, -1, 1, 63058, -7866691]$	\(y^2+xy+y=x^3-x^2+63058x-7866691\)
6942.l2	6942n1	6942.l	6942n	$3$	$9$	\( 2 \cdot 3 \cdot 13 \cdot 89 \)	\( - 2^{18} \cdot 3^{9} \cdot 13^{3} \cdot 89 \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$65664$	$1.799290$	$-1026784744653907139473/1008907331567616$	$[1, 0, 0, -210177, 37101321]$	\(y^2+xy=x^3-210177x+37101321\)
15810.u1	15810u1	15810.u	15810u	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 31 \)	\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 17^{2} \cdot 31^{3} \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1.001590490$	$1$		$26$	$1329696$	$2.972321$	$-4888687926204690735691893601/169462737117000000000$	$[1, 0, 0, -35358150, 80924422500]$	\(y^2+xy=x^3-35358150x+80924422500\)
17670.z3	17670bb1	17670.z	17670bb	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 31 \)	\( 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19 \cdot 31^{3} \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$427680$	$2.429310$	$350792849898814825511281/11141148807000000000$	$[1, 0, 0, -1469295, 666308025]$	\(y^2+xy=x^3-1469295x+666308025\)
35910.by1	35910bt3	35910.by	35910bt	$3$	$9$	\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{9} \cdot 7^{3} \cdot 19 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.5	3B.1.1	$1.798177555$	$1$		$22$	$1259712$	$2.447514$	$-21351492553819653671547/3336704000000000$	$[1, -1, 1, -3606647, 2637610319]$	\(y^2+xy+y=x^3-x^2-3606647x+2637610319\)
60990.bh2	60990bj1	60990.bh	60990bj	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 107 \)	\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19^{3} \cdot 107 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$2.495055653$	$1$		$18$	$1469664$	$2.358532$	$-1367453954870275397761/14445609579000000000$	$[1, 0, 0, -231240, 187785792]$	\(y^2+xy=x^3-231240x+187785792\)
83370.x2	83370x1	83370.x	83370x	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 397 \)	\( - 2^{27} \cdot 3^{9} \cdot 5^{9} \cdot 7^{6} \cdot 397 \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$39424320$	$3.742001$	$-3626272648660625410108067281/240996070457081856000000000$	$[1, 0, 0, -32007045, 750143318337]$	\(y^2+xy=x^3-32007045x+750143318337\)
92910.bd2	92910bi1	92910.bd	92910bi	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 19 \cdot 163 \)	\( - 2^{9} \cdot 3^{9} \cdot 5^{9} \cdot 19^{3} \cdot 163 \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$3394224$	$2.472027$	$-433836620224795849583521/22005928611000000000$	$[1, 0, 0, -1577130, 794918052]$	\(y^2+xy=x^3-1577130x+794918052\)
118698.f3	118698i1	118698.f	118698i	$3$	$9$	\( 2 \cdot 3 \cdot 73 \cdot 271 \)	\( 2^{27} \cdot 3^{18} \cdot 73^{3} \cdot 271 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$5.522076526$	$1$		$14$	$69004224$	$3.830963$	$139690200244171980376257072833953/5481890282879036260614144$	$[1, 0, 0, -1080971082, 13678914712356]$	\(y^2+xy=x^3-1080971082x+13678914712356\)
122094.be2	122094bl3	122094.be	122094bl	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \cdot 17 \cdot 19 \)	\( 2^{27} \cdot 3^{5} \cdot 7^{9} \cdot 17 \cdot 19^{3} \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$31492800$	$3.449272$	$3272351648557113352874597691/631541606162039308288$	$[1, -1, 1, -193010459, 1031970436427]$	\(y^2+xy+y=x^3-x^2-193010459x+1031970436427\)
128226.s3	128226ba1	128226.s	128226ba	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 43 \cdot 71 \)	\( 2^{9} \cdot 3^{9} \cdot 7^{9} \cdot 43^{3} \cdot 71 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$2.128858521$	$1$		$18$	$16796160$	$2.999702$	$1544204814149745316374461713/2295658741816117891584$	$[1, 0, 0, -24080217, 45421448121]$	\(y^2+xy=x^3-24080217x+45421448121\)
129162.bf3	129162bh1	129162.bf	129162bh	$3$	$9$	\( 2 \cdot 3 \cdot 11 \cdot 19 \cdot 103 \)	\( 2^{9} \cdot 3^{18} \cdot 11^{9} \cdot 19 \cdot 103^{3} \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$100745856$	$4.063385$	$19687440505944790974585155384593/9710732423439397326945222144$	$[1, 0, 0, -562542297, 1973424349881]$	\(y^2+xy=x^3-562542297x+1973424349881\)
143430.u2	143430b1	143430.u	143430b	$3$	$9$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 683 \)	\( - 2^{27} \cdot 3^{9} \cdot 5^{9} \cdot 7^{6} \cdot 683 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1.851792099$	$1$		$22$	$87340032$	$3.886715$	$-14313500104002032435046925025521/414610368065961984000000000$	$[1, 0, 0, -505833255, 4487049903177]$	\(y^2+xy=x^3-505833255x+4487049903177\)
357378.l3	357378l1	357378.l	357378l	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 67 \cdot 127 \)	\( - 2^{9} \cdot 3^{18} \cdot 7^{9} \cdot 67^{3} \cdot 127 \)	$0$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$1$	$1$		$8$	$217323648$	$3.771526$	$527737231583370421518916605167/305747584820092901684491776$	$[1, 0, 0, 168357063, -28208561031]$	\(y^2+xy=x^3+168357063x-28208561031\)
402522.g1	402522g1	402522.g	402522g	$3$	$9$	\( 2 \cdot 3 \cdot 73 \cdot 919 \)	\( - 2^{27} \cdot 3^{18} \cdot 73^{3} \cdot 919 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.5	3B.1.1	$13.16387443$	$1$		$8$	$446497920$	$4.131203$	$-15726464326139854896588126629981953/18589878855962488278614016$	$[1, 0, 0, -5219582832, 145144621322496]$	\(y^2+xy=x^3-5219582832x+145144621322496\)
417690.cy3	417690cy2	417690.cy	417690cy	$3$	$9$	\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 17 \)	\( - 2^{9} \cdot 3^{5} \cdot 5^{9} \cdot 7^{9} \cdot 13^{3} \cdot 17 \)	$1$	$\Z/9\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.72.0.5	3B.1.1	$2.144954042$	$1$		$22$	$85660416$	$3.204266$	$397090089854833871209893/1507166867843000000000$	$[1, -1, 1, 9555583, 26802839441]$	\(y^2+xy+y=x^3-x^2+9555583x+26802839441\)