Elliptic curves over $\Q$ of conductor 6069

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
6069.a1	6069a1	6069.a	6069a	$1$	$1$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3^{7} \cdot 7^{2} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.439005330$	$1$		$4$	$32256$	$1.338800$	$-8390176768/1821771$	$0.90870$	$4.61123$	$[0, -1, 1, -12234, 614882]$	\(y^2+y=x^3-x^2-12234x+614882\)	102.2.0.?	$[(125, 1011)]$
6069.b1	6069b5	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( 3 \cdot 7^{2} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$5712$	$192$	$1$	$1$	$4$	$2$	$0$	$18432$	$1.490812$	$53297461115137/147$	$1.05087$	$5.57990$	$[1, 1, 1, -226582, -41607616]$	\(y^2+xy+y=x^3+x^2-226582x-41607616\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[]$
6069.b2	6069b3	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( 3^{2} \cdot 7^{4} \cdot 17^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.18	2Cs	$2856$	$192$	$1$	$1$	$1$		$2$	$9216$	$1.144238$	$13027640977/21609$	$1.08149$	$4.62517$	$[1, 1, 1, -14167, -654004]$	\(y^2+xy+y=x^3+x^2-14167x-654004\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$	$[]$
6069.b3	6069b4	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( 3^{8} \cdot 7 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$5712$	$192$	$1$	$1$	$1$		$0$	$9216$	$1.144238$	$6570725617/45927$	$1.00160$	$4.54660$	$[1, 1, 1, -11277, 453444]$	\(y^2+xy+y=x^3+x^2-11277x+453444\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[]$
6069.b4	6069b6	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3 \cdot 7^{8} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$5712$	$192$	$1$	$1$	$1$		$0$	$18432$	$1.490812$	$-4354703137/17294403$	$1.04266$	$4.73610$	$[1, 1, 1, -9832, -1056292]$	\(y^2+xy+y=x^3+x^2-9832x-1056292\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[]$
6069.b5	6069b2	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( 3^{4} \cdot 7^{2} \cdot 17^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.10	2Cs	$2856$	$192$	$1$	$1$	$1$		$2$	$4608$	$0.797665$	$7189057/3969$	$1.14862$	$3.76392$	$[1, 1, 1, -1162, -3754]$	\(y^2+xy+y=x^3+x^2-1162x-3754\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[]$
6069.b6	6069b1	6069.b	6069b	$6$	$8$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3^{2} \cdot 7 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.1	2B	$5712$	$192$	$1$	$1$	$1$		$1$	$2304$	$0.451091$	$103823/63$	$0.97868$	$3.27745$	$[1, 1, 1, 283, -286]$	\(y^2+xy+y=x^3+x^2+283x-286\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[]$
6069.c1	6069d1	6069.c	6069d	$1$	$1$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3 \cdot 7^{4} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1$	$1$		$0$	$9216$	$1.075993$	$-16777216/122451$	$1.06893$	$4.16094$	$[0, 1, 1, -1541, -86446]$	\(y^2+y=x^3+x^2-1541x-86446\)	102.2.0.?	$[]$
6069.d1	6069e1	6069.d	6069e	$1$	$1$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3^{17} \cdot 7^{4} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.225098426$	$1$		$6$	$156672$	$2.544430$	$5009339741732864/5271114033171$	$1.04955$	$6.10144$	$[0, 1, 1, 1030189, 364409024]$	\(y^2+y=x^3+x^2+1030189x+364409024\)	102.2.0.?	$[(334, 27310)]$
6069.e1	6069c1	6069.e	6069c	$1$	$1$	\( 3 \cdot 7 \cdot 17^{2} \)	\( - 3 \cdot 7^{2} \cdot 17^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1$	$1$		$0$	$13824$	$1.228355$	$841232384/722211$	$0.90829$	$4.31063$	$[0, -1, 1, 5684, -116577]$	\(y^2+y=x^3-x^2+5684x-116577\)	102.2.0.?	$[]$