Elliptic curves over $\Q$ of conductor 4730

Results (22 matches)

  Download displayed columns for results to

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
4730.a1	4730c2	4730.a	4730c	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{9} \cdot 5^{2} \cdot 11^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18920$	$12$	$0$	$1$	$1$		$0$	$13536$	$1.290184$	$179028606517430416921/66598400$	$0.96308$	$5.51121$	$[1, 0, 1, -117418, 15476508]$	\(y^2+xy+y=x^3-117418x+15476508\)	2.3.0.a.1, 220.6.0.?, 344.6.0.?, 18920.12.0.?	$[]$
4730.a2	4730c1	4730.a	4730c	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{18} \cdot 5 \cdot 11 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18920$	$12$	$0$	$1$	$1$		$1$	$6768$	$0.943610$	$-43688964783576601/26658734080$	$0.92351$	$4.52829$	$[1, 0, 1, -7338, 241436]$	\(y^2+xy+y=x^3-7338x+241436\)	2.3.0.a.1, 110.6.0.?, 344.6.0.?, 18920.12.0.?	$[]$
4730.b1	4730a2	4730.b	4730a	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{2} \cdot 5^{2} \cdot 11 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$9460$	$12$	$0$	$0.470693659$	$1$		$8$	$1152$	$0.110729$	$1348866350649/2033900$	$0.96623$	$3.30080$	$[1, -1, 0, -230, 1400]$	\(y^2+xy=x^3-x^2-230x+1400\)	2.3.0.a.1, 44.6.0.a.1, 860.6.0.?, 9460.12.0.?	$[(10, 0)]$
4730.b2	4730a1	4730.b	4730a	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{4} \cdot 5 \cdot 11^{2} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$9460$	$12$	$0$	$0.941387318$	$1$		$5$	$576$	$-0.235844$	$-116930169/416240$	$0.88758$	$2.42793$	$[1, -1, 0, -10, 36]$	\(y^2+xy=x^3-x^2-10x+36\)	2.3.0.a.1, 44.6.0.b.1, 430.6.0.?, 9460.12.0.?	$[(0, 6)]$
4730.c1	4730b3	4730.c	4730b	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{4} \cdot 5^{8} \cdot 11^{3} \cdot 43^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$3784$	$48$	$0$	$2.013886990$	$1$		$8$	$30720$	$1.894001$	$288464247626448102201/28440150818750000$	$1.06358$	$5.56758$	$[1, -1, 0, -137654, 17939460]$	\(y^2+xy=x^3-x^2-137654x+17939460\)	2.3.0.a.1, 4.12.0-4.c.1.1, 44.24.0-44.h.1.2, 344.24.0.?, 3784.48.0.?	$[(296, 1602)]$
4730.c2	4730b2	4730.c	4730b	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{8} \cdot 5^{4} \cdot 11^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1892$	$48$	$0$	$4.027773980$	$1$		$4$	$15360$	$1.547426$	$3350496292255693881/524098606240000$	$1.08368$	$5.04104$	$[1, -1, 0, -31174, -1801932]$	\(y^2+xy=x^3-x^2-31174x-1801932\)	2.6.0.a.1, 4.12.0-2.a.1.1, 44.24.0-44.a.1.1, 172.24.0.?, 1892.48.0.?	$[(652, 15634)]$
4730.c3	4730b1	4730.c	4730b	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{16} \cdot 5^{2} \cdot 11^{3} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$3784$	$48$	$0$	$8.055547960$	$1$		$1$	$7680$	$1.200853$	$2954499865542011961/93770547200$	$0.96618$	$5.02617$	$[1, -1, 0, -29894, -1981900]$	\(y^2+xy=x^3-x^2-29894x-1981900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 44.12.0-4.c.1.2, 88.24.0.?, $\ldots$	$[(76796/19, 6944678/19)]$
4730.c4	4730b4	4730.c	4730b	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{4} \cdot 5^{2} \cdot 11^{12} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$3784$	$48$	$0$	$8.055547960$	$1$		$0$	$30720$	$1.894001$	$18225478596775570119/53980968079601200$	$1.02285$	$5.40847$	$[1, -1, 0, 54826, -10040732]$	\(y^2+xy=x^3-x^2+54826x-10040732\)	2.3.0.a.1, 4.12.0-4.c.1.2, 86.6.0.?, 88.24.0.?, 172.24.0.?, $\ldots$	$[(5653/3, 436738/3)]$
4730.d1	4730k1	4730.d	4730k	$2$	$7$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{7} \cdot 5^{7} \cdot 11^{7} \cdot 43^{2} \)	$1$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$3080$	$96$	$2$	$0.982057305$	$1$		$20$	$219520$	$2.493233$	$-19237750463016353596082481/360317791790000000$	$1.02313$	$6.88031$	$[1, -1, 1, -5582262, 5077966149]$	\(y^2+xy+y=x^3-x^2-5582262x+5077966149\)	7.48.0-7.a.1.2, 440.2.0.?, 3080.96.2.?	$[(1377, 171)]$
4730.d2	4730k2	4730.d	4730k	$2$	$7$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2 \cdot 5 \cdot 11 \cdot 43^{14} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$3080$	$96$	$2$	$6.874401136$	$1$		$0$	$1536640$	$3.466187$	$7154705394529607961737582319/8127389307855235414199390$	$1.04985$	$7.57977$	$[1, -1, 1, 40144188, -96077802411]$	\(y^2+xy+y=x^3-x^2+40144188x-96077802411\)	7.48.0-7.a.2.2, 440.2.0.?, 3080.96.2.?	$[(188049061/252, 3509939761201/252)]$
4730.e1	4730f1	4730.e	4730f	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{4} \cdot 5^{2} \cdot 11 \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1892$	$2$	$0$	$0.190883427$	$1$		$6$	$448$	$-0.304564$	$-24137569/189200$	$0.88506$	$2.32537$	$[1, 1, 1, -6, 19]$	\(y^2+xy+y=x^3+x^2-6x+19\)	1892.2.0.?	$[(-1, 5)]$
4730.f1	4730d1	4730.f	4730d	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{7} \cdot 5^{3} \cdot 11^{4} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1720$	$2$	$0$	$0.778675984$	$1$		$4$	$3360$	$0.617244$	$-12054670471089/10073008000$	$0.90249$	$3.66524$	$[1, -1, 1, -478, -6163]$	\(y^2+xy+y=x^3-x^2-478x-6163\)	1720.2.0.?	$[(65, 451)]$
4730.g1	4730g4	4730.g	4730g	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2 \cdot 5^{3} \cdot 11 \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$18920$	$48$	$0$	$1$	$4$	$2$	$0$	$18816$	$1.543097$	$27741081432830042816001/118250$	$1.00313$	$6.10720$	$[1, -1, 1, -630667, 192931441]$	\(y^2+xy+y=x^3-x^2-630667x+192931441\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 220.12.0.?, 344.24.0.?, $\ldots$	$[]$
4730.g2	4730g3	4730.g	4730g	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2 \cdot 5^{12} \cdot 11^{4} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$18920$	$48$	$0$	$1$	$1$		$0$	$18816$	$1.543097$	$6996814880788790721/307403808593750$	$1.05543$	$5.12806$	$[1, -1, 1, -39847, 2952969]$	\(y^2+xy+y=x^3-x^2-39847x+2952969\)	2.3.0.a.1, 4.12.0-4.c.1.2, 344.24.0.?, 440.24.0.?, 18920.48.0.?	$[]$
4730.g3	4730g2	4730.g	4730g	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{2} \cdot 5^{6} \cdot 11^{2} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$18920$	$48$	$0$	$1$	$1$		$2$	$9408$	$1.196524$	$6772735026997676001/13983062500$	$1.14277$	$5.12421$	$[1, -1, 1, -39417, 3021941]$	\(y^2+xy+y=x^3-x^2-39417x+3021941\)	2.6.0.a.1, 4.12.0-2.a.1.1, 220.24.0.?, 344.24.0.?, 18920.48.0.?	$[]$
4730.g4	4730g1	4730.g	4730g	$4$	$4$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{4} \cdot 5^{3} \cdot 11 \cdot 43^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$18920$	$48$	$0$	$1$	$1$		$3$	$4704$	$0.849950$	$-1600011920811681/75213622000$	$1.02734$	$4.14656$	$[1, -1, 1, -2437, 48749]$	\(y^2+xy+y=x^3-x^2-2437x+48749\)	2.3.0.a.1, 4.12.0-4.c.1.1, 110.6.0.?, 220.24.0.?, 344.24.0.?, $\ldots$	$[]$
4730.h1	4730e1	4730.h	4730e	$2$	$3$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{24} \cdot 5^{2} \cdot 11 \cdot 43 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$5676$	$16$	$0$	$1.137946771$	$1$		$8$	$5760$	$0.945987$	$-6641385549974209/198390579200$	$0.91330$	$4.31149$	$[1, 0, 0, -3916, 96400]$	\(y^2+xy=x^3-3916x+96400\)	3.8.0-3.a.1.2, 1892.2.0.?, 5676.16.0.?	$[(48, 116)]$
4730.h2	4730e2	4730.h	4730e	$2$	$3$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{8} \cdot 5^{6} \cdot 11^{3} \cdot 43^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$5676$	$16$	$0$	$0.379315590$	$1$		$4$	$17280$	$1.495293$	$628345970980160831/423295268000000$	$0.96089$	$4.84323$	$[1, 0, 0, 17844, 373136]$	\(y^2+xy=x^3+17844x+373136\)	3.8.0-3.a.1.1, 1892.2.0.?, 5676.16.0.?	$[(286, 5232)]$
4730.i1	4730j1	4730.i	4730j	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{9} \cdot 5 \cdot 11 \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$440$	$2$	$0$	$0.343613553$	$1$		$4$	$1152$	$0.161671$	$4733169839/52067840$	$0.85297$	$2.97444$	$[1, 0, 0, 35, -335]$	\(y^2+xy=x^3+35x-335\)	440.2.0.?	$[(12, 37)]$
4730.j1	4730h1	4730.j	4730h	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2 \cdot 5^{5} \cdot 11 \cdot 43^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$440$	$2$	$0$	$1$	$1$		$0$	$3520$	$0.330892$	$-3975097468321/127118750$	$0.93162$	$3.43488$	$[1, 0, 0, -330, -2398]$	\(y^2+xy=x^3-330x-2398\)	440.2.0.?	$[]$
4730.k1	4730i2	4730.k	4730i	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( 2^{7} \cdot 5^{22} \cdot 11^{2} \cdot 43^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18920$	$12$	$0$	$1$	$1$		$0$	$850080$	$3.397671$	$8846316694484611683132528001/2935896911621093750000000$	$1.02535$	$7.60485$	$[1, 1, 1, -43087000, 71076326617]$	\(y^2+xy+y=x^3+x^2-43087000x+71076326617\)	2.3.0.a.1, 220.6.0.?, 344.6.0.?, 18920.12.0.?	$[]$
4730.k2	4730i1	4730.k	4730i	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 43 \)	\( - 2^{14} \cdot 5^{11} \cdot 11 \cdot 43^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$18920$	$12$	$0$	$1$	$1$		$1$	$425040$	$3.051098$	$52430803961239418232136319/55627994831200000000000$	$1.01712$	$6.99879$	$[1, 1, 1, 7797480, 7653910745]$	\(y^2+xy+y=x^3+x^2+7797480x+7653910745\)	2.3.0.a.1, 110.6.0.?, 344.6.0.?, 18920.12.0.?	$[]$

  Download displayed columns for results to