Elliptic curve search results

Results (25 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	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1005.b1	1005a1	1005.b	1005a	$2$	$2$	\( 3 \cdot 5 \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$360$	$0.353420$	$2912566550041/254390625$	$0.91283$	$4.15176$	$[1, 1, 0, -297, -1944]$	\(y^2+xy=x^3+x^2-297x-1944\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
3015.a1	3015a1	3015.a	3015a	$2$	$2$	\( 3^{2} \cdot 5 \cdot 67 \)	\( 3^{11} \cdot 5^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$2880$	$0.902726$	$2912566550041/254390625$	$0.91283$	$4.40521$	$[1, -1, 1, -2678, 49812]$	\(y^2+xy+y=x^3-x^2-2678x+49812\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
5025.b1	5025e1	5025.b	5025e	$2$	$2$	\( 3 \cdot 5^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{12} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.113526827$	$1$		$7$	$8640$	$1.158140$	$2912566550041/254390625$	$0.91283$	$4.50081$	$[1, 0, 0, -7438, -228133]$	\(y^2+xy=x^3-7438x-228133\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(-43, 134)]$
15075.l1	15075i1	15075.l	15075i	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 67 \)	\( 3^{11} \cdot 5^{12} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$3.050602406$	$1$		$1$	$69120$	$1.707445$	$2912566550041/254390625$	$0.91283$	$4.67200$	$[1, -1, 0, -66942, 6159591]$	\(y^2+xy=x^3-x^2-66942x+6159591\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(1191/2, 27159/2)]$
16080.u1	16080y1	16080.u	16080y	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 67 \)	\( 2^{12} \cdot 3^{5} \cdot 5^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$0.252098014$	$1$		$13$	$23040$	$1.046568$	$2912566550041/254390625$	$0.91283$	$3.82205$	$[0, 1, 0, -4760, 114900]$	\(y^2=x^3+x^2-4760x+114900\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(70, 360)]$
48240.n1	48240bp1	48240.n	48240bp	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 67 \)	\( 2^{12} \cdot 3^{11} \cdot 5^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$184320$	$1.595873$	$2912566550041/254390625$	$0.91283$	$4.04393$	$[0, 0, 0, -42843, -3145142]$	\(y^2=x^3-42843x-3145142\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
49245.x1	49245t1	49245.x	49245t	$2$	$2$	\( 3 \cdot 5 \cdot 7^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 7^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$2.302728565$	$1$		$3$	$138240$	$1.326376$	$2912566550041/254390625$	$0.91283$	$3.73689$	$[1, 0, 1, -14579, 623081]$	\(y^2+xy+y=x^3-14579x+623081\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(249, 3403)]$
64320.i1	64320bo1	64320.i	64320bo	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 67 \)	\( 2^{18} \cdot 3^{5} \cdot 5^{6} \cdot 67 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$6.890234960$	$1$		$11$	$184320$	$1.393141$	$2912566550041/254390625$	$0.91283$	$3.71912$	$[0, -1, 0, -19041, 938241]$	\(y^2=x^3-x^2-19041x+938241\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(29, 640), (125, 704)]$
64320.bw1	64320ba1	64320.bw	64320ba	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 67 \)	\( 2^{18} \cdot 3^{5} \cdot 5^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.603419971$	$1$		$5$	$184320$	$1.393141$	$2912566550041/254390625$	$0.91283$	$3.71912$	$[0, 1, 0, -19041, -938241]$	\(y^2=x^3+x^2-19041x-938241\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(-93, 192)]$
67335.e1	67335h1	67335.e	67335h	$2$	$2$	\( 3 \cdot 5 \cdot 67^{2} \)	\( 3^{5} \cdot 5^{6} \cdot 67^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.933314959$	$1$		$3$	$1615680$	$2.455769$	$2912566550041/254390625$	$0.91283$	$4.85078$	$[1, 0, 0, -1335571, 547309040]$	\(y^2+xy=x^3-1335571x+547309040\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(4796, 320810)]$
80400.u1	80400bp1	80400.u	80400bp	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 67 \)	\( 2^{12} \cdot 3^{5} \cdot 5^{12} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$552960$	$1.851286$	$2912566550041/254390625$	$0.91283$	$4.13240$	$[0, -1, 0, -119008, 14600512]$	\(y^2=x^3-x^2-119008x+14600512\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
121605.c1	121605g1	121605.c	121605g	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 11^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.192999418$	$1$		$7$	$518400$	$1.552368$	$2912566550041/254390625$	$0.91283$	$3.68000$	$[1, 1, 1, -36000, 2407560]$	\(y^2+xy+y=x^3+x^2-36000x+2407560\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(138, 233)]$
147735.q1	147735i1	147735.q	147735i	$2$	$2$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 67 \)	\( 3^{11} \cdot 5^{6} \cdot 7^{6} \cdot 67 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$2.752219798$	$1$		$15$	$1105920$	$1.875681$	$2912566550041/254390625$	$0.91283$	$3.94577$	$[1, -1, 1, -131207, -16823194]$	\(y^2+xy+y=x^3-x^2-131207x-16823194\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(576, 9634), (-204, 1294)]$
169845.f1	169845o1	169845.f	169845o	$2$	$2$	\( 3 \cdot 5 \cdot 13^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 13^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$777600$	$1.635895$	$2912566550041/254390625$	$0.91283$	$3.66114$	$[1, 1, 1, -50281, -4019722]$	\(y^2+xy+y=x^3+x^2-50281x-4019722\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
192960.ei1	192960dn1	192960.ei	192960dn	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 67 \)	\( 2^{18} \cdot 3^{11} \cdot 5^{6} \cdot 67 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.747583730$	$1$		$19$	$1474560$	$1.942448$	$2912566550041/254390625$	$0.91283$	$3.92502$	$[0, 0, 0, -171372, 25161136]$	\(y^2=x^3-171372x+25161136\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(152, 1620), (-10, 5184)]$
192960.ej1	192960m1	192960.ej	192960m	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 67 \)	\( 2^{18} \cdot 3^{11} \cdot 5^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$1474560$	$1.942448$	$2912566550041/254390625$	$0.91283$	$3.92502$	$[0, 0, 0, -171372, -25161136]$	\(y^2=x^3-171372x-25161136\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
202005.j1	202005j1	202005.j	202005j	$2$	$2$	\( 3^{2} \cdot 5 \cdot 67^{2} \)	\( 3^{11} \cdot 5^{6} \cdot 67^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$12925440$	$3.005074$	$2912566550041/254390625$	$0.91283$	$4.95413$	$[1, -1, 0, -12020139, -14777344080]$	\(y^2+xy=x^3-x^2-12020139x-14777344080\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
241200.dn1	241200dn1	241200.dn	241200dn	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 67 \)	\( 2^{12} \cdot 3^{11} \cdot 5^{12} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$4.029269496$	$1$		$3$	$4423680$	$2.400593$	$2912566550041/254390625$	$0.91283$	$4.29795$	$[0, 0, 0, -1071075, -393142750]$	\(y^2=x^3-1071075x-393142750\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(2785, 135000)]$
246225.r1	246225r1	246225.r	246225r	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{12} \cdot 7^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$4.665048179$	$1$		$3$	$3317760$	$2.131096$	$2912566550041/254390625$	$0.91283$	$4.03030$	$[1, 1, 1, -364463, 77885156]$	\(y^2+xy+y=x^3+x^2-364463x+77885156\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(706, 12803)]$
290445.e1	290445e1	290445.e	290445e	$2$	$2$	\( 3 \cdot 5 \cdot 17^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 17^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$1774080$	$1.770027$	$2912566550041/254390625$	$0.91283$	$3.63294$	$[1, 0, 1, -85984, -8949343]$	\(y^2+xy+y=x^3-85984x-8949343\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
321600.cu1	321600cu1	321600.cu	321600cu	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 67 \)	\( 2^{18} \cdot 3^{5} \cdot 5^{12} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$8.911418481$	$1$		$1$	$4423680$	$2.197861$	$2912566550041/254390625$	$0.91283$	$4.00860$	$[0, -1, 0, -476033, -116328063]$	\(y^2=x^3-x^2-476033x-116328063\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(293113/3, 158652800/3)]$
321600.hb1	321600hb1	321600.hb	321600hb	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 67 \)	\( 2^{18} \cdot 3^{5} \cdot 5^{12} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$4423680$	$2.197861$	$2912566550041/254390625$	$0.91283$	$4.00860$	$[0, 1, 0, -476033, 116328063]$	\(y^2=x^3+x^2-476033x+116328063\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
336675.z1	336675z1	336675.z	336675z	$2$	$2$	\( 3 \cdot 5^{2} \cdot 67^{2} \)	\( 3^{5} \cdot 5^{12} \cdot 67^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$38776320$	$3.260487$	$2912566550041/254390625$	$0.91283$	$4.99611$	$[1, 1, 0, -33389275, 68413630000]$	\(y^2+xy=x^3+x^2-33389275x+68413630000\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
362805.e1	362805e1	362805.e	362805e	$2$	$2$	\( 3 \cdot 5 \cdot 19^{2} \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 19^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$0.509892038$	$1$		$7$	$2488320$	$1.825640$	$2912566550041/254390625$	$0.91283$	$3.62194$	$[1, 0, 0, -107405, 12475152]$	\(y^2+xy=x^3-107405x+12475152\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(49, 2683)]$
364815.z1	364815z1	364815.z	364815z	$2$	$2$	\( 3^{2} \cdot 5 \cdot 11^{2} \cdot 67 \)	\( 3^{11} \cdot 5^{6} \cdot 11^{6} \cdot 67 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4020$	$12$	$0$	$5.190101625$	$1$		$3$	$4147200$	$2.101673$	$2912566550041/254390625$	$0.91283$	$3.87901$	$[1, -1, 0, -324000, -65328125]$	\(y^2+xy=x^3-x^2-324000x-65328125\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(21750, 3195625)]$