Elliptic curves over $\Q$ of conductor 2842

Results (10 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
2842.a1	2842b2	2842.a	2842b	$2$	$2$	\( 2 \cdot 7^{2} \cdot 29 \)	\( 2^{8} \cdot 7^{16} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$812$	$12$	$0$	$1$	$1$		$0$	$61440$	$2.313015$	$6684374974140996553/2097096248576$	$1.00277$	$6.91901$	$[1, 0, 1, -1922982, 1025947640]$	\(y^2+xy+y=x^3-1922982x+1025947640\)	2.3.0.a.1, 28.6.0.c.1, 58.6.0.a.1, 812.12.0.?	$[]$
2842.a2	2842b1	2842.a	2842b	$2$	$2$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{16} \cdot 7^{11} \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$812$	$12$	$0$	$1$	$1$		$1$	$30720$	$1.966442$	$-1060490285861833/926330847232$	$0.97586$	$5.93454$	$[1, 0, 1, -104102, 20470776]$	\(y^2+xy+y=x^3-104102x+20470776\)	2.3.0.a.1, 14.6.0.b.1, 116.6.0.?, 812.12.0.?	$[]$
2842.b1	2842d1	2842.b	2842d	$2$	$3$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{4} \cdot 7^{8} \cdot 29^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2436$	$16$	$0$	$0.555979013$	$1$		$4$	$4608$	$1.050020$	$-338608873/19120976$	$0.94038$	$4.51528$	$[1, 1, 0, -711, -72827]$	\(y^2+xy=x^3+x^2-711x-72827\)	3.4.0.a.1, 21.8.0-3.a.1.1, 116.2.0.?, 348.8.0.?, 2436.16.0.?	$[(202, 2741)]$
2842.b2	2842d2	2842.b	2842d	$2$	$3$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{12} \cdot 7^{12} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2436$	$16$	$0$	$1.667937040$	$1$		$2$	$13824$	$1.599325$	$245667233447/13974818816$	$0.98609$	$5.34194$	$[1, 1, 0, 6394, 1943572]$	\(y^2+xy=x^3+x^2+6394x+1943572\)	3.4.0.a.1, 21.8.0-3.a.1.2, 116.2.0.?, 348.8.0.?, 2436.16.0.?	$[(188, 3042)]$
2842.c1	2842a2	2842.c	2842a	$2$	$2$	\( 2 \cdot 7^{2} \cdot 29 \)	\( 2^{5} \cdot 7^{12} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1624$	$12$	$0$	$1$	$4$	$2$	$0$	$11520$	$1.686041$	$13350003080765625/109178272$	$1.22373$	$6.13734$	$[1, -1, 0, -242167, -45808323]$	\(y^2+xy=x^3-x^2-242167x-45808323\)	2.3.0.a.1, 28.6.0.c.1, 232.6.0.?, 1624.12.0.?	$[]$
2842.c2	2842a1	2842.c	2842a	$2$	$2$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{10} \cdot 7^{9} \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1624$	$12$	$0$	$1$	$1$		$1$	$5760$	$1.339468$	$-3051779837625/295386112$	$1.14571$	$5.10256$	$[1, -1, 0, -14807, -745571]$	\(y^2+xy=x^3-x^2-14807x-745571\)	2.3.0.a.1, 14.6.0.b.1, 232.6.0.?, 1624.12.0.?	$[]$
2842.d1	2842c1	2842.d	2842c	$1$	$1$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{2} \cdot 7^{6} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$1$	$1$		$0$	$1440$	$0.070727$	$-185193/116$	$0.85122$	$3.08568$	$[1, -1, 0, -58, -232]$	\(y^2+xy=x^3-x^2-58x-232\)	116.2.0.?	$[]$
2842.e1	2842e2	2842.e	2842e	$2$	$5$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{2} \cdot 7^{6} \cdot 29^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$4060$	$48$	$1$	$1.721561078$	$1$		$2$	$7200$	$1.320120$	$-10418796526321/82044596$	$0.99481$	$5.23921$	$[1, 0, 0, -22296, 1288244]$	\(y^2+xy=x^3-22296x+1288244\)	5.12.0.a.2, 35.24.0-5.a.2.2, 116.2.0.?, 580.24.1.?, 4060.48.1.?	$[(88, 54)]$
2842.e2	2842e1	2842.e	2842e	$2$	$5$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{10} \cdot 7^{6} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$4060$	$48$	$1$	$0.344312215$	$1$		$6$	$1440$	$0.515400$	$13651919/29696$	$1.08166$	$3.66181$	$[1, 0, 0, 244, -2416]$	\(y^2+xy=x^3+244x-2416\)	5.12.0.a.1, 35.24.0-5.a.1.2, 116.2.0.?, 580.24.1.?, 4060.48.1.?	$[(32, 180)]$
2842.f1	2842f1	2842.f	2842f	$1$	$1$	\( 2 \cdot 7^{2} \cdot 29 \)	\( - 2^{8} \cdot 7^{8} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$1$	$1$		$0$	$3072$	$0.908002$	$-117433042273/363776$	$0.89932$	$4.67413$	$[1, 0, 0, -4999, -136823]$	\(y^2+xy=x^3-4999x-136823\)	116.2.0.?	$[]$