Elliptic curve search results

Results (32 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
930.n2	930n3	930.n	930n	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$1$	$4320$	$1.458746$	$-6894246873502147249/47925198774000$	$[1, 0, 0, -39651, -3060495]$	\(y^2+xy=x^3-39651x-3060495\)
2790.k2	2790l3	2790.k	2790l	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5 \cdot 31 \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$5$	$34560$	$2.008053$	$-6894246873502147249/47925198774000$	$[1, -1, 0, -356859, 82633365]$	\(y^2+xy=x^3-x^2-356859x+82633365\)
4650.d2	4650f3	4650.d	4650f	$4$	$6$	\( 2 \cdot 3 \cdot 5^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{9} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$103680$	$2.263466$	$-6894246873502147249/47925198774000$	$[1, 1, 0, -991275, -382561875]$	\(y^2+xy=x^3+x^2-991275x-382561875\)
7440.b2	7440i3	7440.b	7440i	$4$	$6$	\( 2^{4} \cdot 3 \cdot 5 \cdot 31 \)	\( - 2^{16} \cdot 3^{3} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$103680$	$2.151894$	$-6894246873502147249/47925198774000$	$[0, -1, 0, -634416, 195871680]$	\(y^2=x^3-x^2-634416x+195871680\)
13950.bw2	13950cp3	13950.bw	13950cp	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{9} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$829440$	$2.812771$	$-6894246873502147249/47925198774000$	$[1, -1, 1, -8921480, 10320249147]$	\(y^2+xy+y=x^3-x^2-8921480x+10320249147\)
22320.bi2	22320bv3	22320.bi	22320bv	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( - 2^{16} \cdot 3^{9} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$829440$	$2.701199$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -5709747, -5282825614]$	\(y^2=x^3-5709747x-5282825614\)
28830.z2	28830z3	28830.z	28830z	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 31^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$16.54857054$	$1$		$1$	$4147200$	$3.175739$	$-6894246873502147249/47925198774000$	$[1, 1, 1, -38104631, 91060892669]$	\(y^2+xy+y=x^3+x^2-38104631x+91060892669\)
29760.bj2	29760s3	29760.bj	29760s	$4$	$6$	\( 2^{6} \cdot 3 \cdot 5 \cdot 31 \)	\( - 2^{22} \cdot 3^{3} \cdot 5^{3} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$5.434469664$	$1$		$3$	$829440$	$2.498466$	$-6894246873502147249/47925198774000$	$[0, -1, 0, -2537665, -1564435775]$	\(y^2=x^3-x^2-2537665x-1564435775\)
29760.co2	29760cv3	29760.co	29760cv	$4$	$6$	\( 2^{6} \cdot 3 \cdot 5 \cdot 31 \)	\( - 2^{22} \cdot 3^{3} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$829440$	$2.498466$	$-6894246873502147249/47925198774000$	$[0, 1, 0, -2537665, 1564435775]$	\(y^2=x^3+x^2-2537665x+1564435775\)
37200.dm2	37200ct3	37200.dm	37200ct	$4$	$6$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( - 2^{16} \cdot 3^{3} \cdot 5^{9} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$2.217308066$	$1$		$3$	$2488320$	$2.956612$	$-6894246873502147249/47925198774000$	$[0, 1, 0, -15860408, 24452239188]$	\(y^2=x^3+x^2-15860408x+24452239188\)
45570.ch2	45570cb3	45570.ch	45570cb	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$1555200$	$2.431702$	$-6894246873502147249/47925198774000$	$[1, 1, 1, -1942900, 1047806885]$	\(y^2+xy+y=x^3+x^2-1942900x+1047806885\)
86490.bj2	86490bf3	86490.bj	86490bf	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5 \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \cdot 31^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$16$	$2$	$1$	$33177600$	$3.725044$	$-6894246873502147249/47925198774000$	$[1, -1, 0, -342941679, -2458987043747]$	\(y^2+xy=x^3-x^2-342941679x-2458987043747\)
89280.r2	89280eg3	89280.r	89280eg	$4$	$6$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( - 2^{22} \cdot 3^{9} \cdot 5^{3} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$20.97722965$	$1$		$1$	$6635520$	$3.047771$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -22838988, -42262604912]$	\(y^2=x^3-22838988x-42262604912\)
89280.ch2	89280bq3	89280.ch	89280bq	$4$	$6$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( - 2^{22} \cdot 3^{9} \cdot 5^{3} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4.052442392$	$1$		$3$	$6635520$	$3.047771$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -22838988, 42262604912]$	\(y^2=x^3-22838988x+42262604912\)
111600.fq2	111600du3	111600.fq	111600du	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( - 2^{16} \cdot 3^{9} \cdot 5^{9} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$24.41109183$	$1$		$1$	$19906560$	$3.505917$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -142743675, -660353201750]$	\(y^2=x^3-142743675x-660353201750\)
112530.w2	112530bb3	112530.w	112530bb	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 11^{6} \cdot 31^{6} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$2.771567953$	$1$		$15$	$6220800$	$2.657692$	$-6894246873502147249/47925198774000$	$[1, 0, 1, -4797774, 4068721072]$	\(y^2+xy+y=x^3-4797774x+4068721072\)
136710.bb2	136710fb3	136710.bb	136710fb	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \cdot 7^{6} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$32.30037999$	$1$		$1$	$12441600$	$2.981007$	$-6894246873502147249/47925198774000$	$[1, -1, 0, -17486100, -28308272000]$	\(y^2+xy=x^3-x^2-17486100x-28308272000\)
144150.br2	144150di3	144150.br	144150di	$4$	$6$	\( 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{9} \cdot 31^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$5.032423511$	$1$		$3$	$99532800$	$3.980457$	$-6894246873502147249/47925198774000$	$[1, 0, 1, -952615776, 11384516815198]$	\(y^2+xy+y=x^3-952615776x+11384516815198\)
148800.eb2	148800fh3	148800.eb	148800fh	$4$	$6$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( - 2^{22} \cdot 3^{3} \cdot 5^{9} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$19906560$	$3.303185$	$-6894246873502147249/47925198774000$	$[0, -1, 0, -63441633, 195681355137]$	\(y^2=x^3-x^2-63441633x+195681355137\)
148800.ha2	148800hj3	148800.ha	148800hj	$4$	$6$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( - 2^{22} \cdot 3^{3} \cdot 5^{9} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$6.046378682$	$1$		$5$	$19906560$	$3.303185$	$-6894246873502147249/47925198774000$	$[0, 1, 0, -63441633, -195681355137]$	\(y^2=x^3+x^2-63441633x-195681355137\)
157170.bj2	157170bz3	157170.bj	157170bz	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 13^{6} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$7.957334719$	$1$		$3$	$9331200$	$2.741219$	$-6894246873502147249/47925198774000$	$[1, 0, 1, -6701023, -6717206494]$	\(y^2+xy+y=x^3-6701023x-6717206494\)
227850.dr2	227850gj3	227850.dr	227850gj	$4$	$6$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{9} \cdot 7^{6} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4.781497836$	$1$		$3$	$37324800$	$3.236420$	$-6894246873502147249/47925198774000$	$[1, 0, 1, -48572501, 131073005648]$	\(y^2+xy+y=x^3-48572501x+131073005648\)
230640.bx2	230640bx3	230640.bx	230640bx	$4$	$6$	\( 2^{4} \cdot 3 \cdot 5 \cdot 31^{2} \)	\( - 2^{16} \cdot 3^{3} \cdot 5^{3} \cdot 31^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$9$	$3$	$1$	$99532800$	$3.868885$	$-6894246873502147249/47925198774000$	$[0, 1, 0, -609674096, -5829116479020]$	\(y^2=x^3+x^2-609674096x-5829116479020\)
268770.bl2	268770bl3	268770.bl	268770bl	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 17^{6} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$10.31789854$	$1$		$3$	$19906560$	$2.875351$	$-6894246873502147249/47925198774000$	$[1, 1, 1, -11459145, -15024752793]$	\(y^2+xy+y=x^3+x^2-11459145x-15024752793\)
335730.l2	335730l3	335730.l	335730l	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 19^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$4$	$2$	$1$	$26127360$	$2.930965$	$-6894246873502147249/47925198774000$	$[1, 1, 0, -14314018, 20963307172]$	\(y^2+xy=x^3+x^2-14314018x+20963307172\)
337590.ej2	337590ej3	337590.ej	337590ej	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \cdot 11^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$49766400$	$3.206997$	$-6894246873502147249/47925198774000$	$[1, -1, 1, -43179962, -109855468951]$	\(y^2+xy+y=x^3-x^2-43179962x-109855468951\)
364560.ga2	364560ga3	364560.ga	364560ga	$4$	$6$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)	\( - 2^{16} \cdot 3^{3} \cdot 5^{3} \cdot 7^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$37324800$	$3.124847$	$-6894246873502147249/47925198774000$	$[0, 1, 0, -31086400, -67121813452]$	\(y^2=x^3+x^2-31086400x-67121813452\)
432450.fd2	432450fd3	432450.fd	432450fd	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{9} \cdot 31^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1$	$9$	$3$	$1$	$796262400$	$4.529762$	$-6894246873502147249/47925198774000$	$[1, -1, 1, -8573541980, -307381954010353]$	\(y^2+xy+y=x^3-x^2-8573541980x-307381954010353\)
446400.ew2	446400ew3	446400.ew	446400ew	$4$	$6$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( - 2^{22} \cdot 3^{9} \cdot 5^{9} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1.040794197$	$1$		$7$	$159252480$	$3.852489$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -570974700, 5282825614000]$	\(y^2=x^3-570974700x+5282825614000\)
446400.ok2	446400ok3	446400.ok	446400ok	$4$	$6$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( - 2^{22} \cdot 3^{9} \cdot 5^{9} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$42.28549048$	$1$		$1$	$159252480$	$3.852489$	$-6894246873502147249/47925198774000$	$[0, 0, 0, -570974700, -5282825614000]$	\(y^2=x^3-570974700x-5282825614000\)
471510.cz2	471510cz3	471510.cz	471510cz	$4$	$6$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{9} \cdot 5^{3} \cdot 13^{6} \cdot 31^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4.664719828$	$1$		$3$	$74649600$	$3.290527$	$-6894246873502147249/47925198774000$	$[1, -1, 1, -60309203, 181364575331]$	\(y^2+xy+y=x^3-x^2-60309203x+181364575331\)
491970.co2	491970co3	491970.co	491970co	$4$	$6$	\( 2 \cdot 3 \cdot 5 \cdot 23^{2} \cdot 31 \)	\( - 2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 23^{6} \cdot 31^{6} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1.012517453$	$1$		$17$	$54743040$	$3.026493$	$-6894246873502147249/47925198774000$	$[1, 0, 0, -20975390, 37195091892]$	\(y^2+xy=x^3-20975390x+37195091892\)