Elliptic curves over $\Q$ of conductor 4263

Results (16 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
4263.a1	4263a1	4263.a	4263a	$1$	$1$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{6} \cdot 7^{8} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$58$	$2$	$0$	$0.279477784$	$1$		$8$	$7056$	$0.829657$	$62992384/21141$	$0.85521$	$4.01135$	$[0, -1, 1, -1486, 14790]$	\(y^2+y=x^3-x^2-1486x+14790\)	58.2.0.a.1	$[(82, 661)]$
4263.b1	4263d1	4263.b	4263d	$1$	$1$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{6} \cdot 7^{2} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$58$	$2$	$0$	$0.189900019$	$1$		$8$	$1008$	$-0.143298$	$62992384/21141$	$0.85521$	$2.61439$	$[0, 1, 1, -30, -52]$	\(y^2+y=x^3+x^2-30x-52\)	58.2.0.a.1	$[(-3, 4)]$
4263.c1	4263g3	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{3} \cdot 7^{8} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$9744$	$192$	$1$	$1$	$16$	$2$	$0$	$73728$	$2.263618$	$947531277805646290177/38367$	$1.01996$	$7.17609$	$[1, 0, 0, -10026577, -12221002942]$	\(y^2+xy=x^3-10026577x-12221002942\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.8, $\ldots$	$[]$
4263.c2	4263g5	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{24} \cdot 7^{7} \cdot 29^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$9744$	$192$	$1$	$1$	$1$		$2$	$147456$	$2.610191$	$8471112631466271697/1662662681263647$	$1.00847$	$6.61168$	$[1, 0, 0, -2080982, 939113013]$	\(y^2+xy=x^3-2080982x+939113013\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 28.24.0-28.h.1.2, 48.48.0-48.e.2.18, $\ldots$	$[]$
4263.c3	4263g4	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{12} \cdot 7^{8} \cdot 29^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$4872$	$192$	$1$	$1$	$1$		$2$	$73728$	$2.263618$	$244883173420511137/18418027974129$	$1.08831$	$6.18769$	$[1, 0, 0, -638667, -183296520]$	\(y^2+xy=x^3-638667x-183296520\)	2.6.0.a.1, 4.24.0-4.b.1.2, 24.48.0-24.i.1.32, 28.48.0-28.c.1.2, 168.96.0.?, $\ldots$	$[]$
4263.c4	4263g2	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{6} \cdot 7^{10} \cdot 29^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$4872$	$192$	$1$	$1$	$4$	$2$	$2$	$36864$	$1.917044$	$231331938231569617/1472026689$	$0.98909$	$6.18088$	$[1, 0, 0, -626662, -190991725]$	\(y^2+xy=x^3-626662x-190991725\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.i.2.5, 28.24.0-4.b.1.3, $\ldots$	$[]$
4263.c5	4263g1	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( - 3^{3} \cdot 7^{14} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$9744$	$192$	$1$	$1$	$4$	$2$	$1$	$18432$	$1.570469$	$-53297461115137/4513839183$	$0.94722$	$5.19507$	$[1, 0, 0, -38417, -3106272]$	\(y^2+xy=x^3-38417x-3106272\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0.bz.1, $\ldots$	$[]$
4263.c6	4263g6	4263.c	4263g	$6$	$8$	\( 3 \cdot 7^{2} \cdot 29 \)	\( - 3^{6} \cdot 7^{7} \cdot 29^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.56	2B	$9744$	$192$	$1$	$1$	$1$		$0$	$147456$	$2.610191$	$215015459663151503/2552757445339983$	$1.02586$	$6.52763$	$[1, 0, 0, 611568, -813164913]$	\(y^2+xy=x^3+611568x-813164913\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 14.6.0.b.1, 24.48.0-24.bz.2.6, $\ldots$	$[]$
4263.d1	4263c2	4263.d	4263c	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{6} \cdot 7^{3} \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1.048838222$	$1$		$4$	$1152$	$0.287763$	$1121622319/613089$	$0.94499$	$3.19175$	$[1, 1, 0, -151, 106]$	\(y^2+xy=x^3+x^2-151x+106\)	2.3.0.a.1, 28.6.0.a.1, 348.6.0.?, 2436.12.0.?	$[(-6, 32)]$
4263.d2	4263c1	4263.d	4263c	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{3} \cdot 7^{3} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$2.097676444$	$1$		$3$	$576$	$-0.058810$	$510082399/783$	$0.94444$	$3.09747$	$[1, 1, 0, -116, 435]$	\(y^2+xy=x^3+x^2-116x+435\)	2.3.0.a.1, 28.6.0.b.1, 348.6.0.?, 1218.6.0.?, 2436.12.0.?	$[(10, 15)]$
4263.e1	4263e2	4263.e	4263e	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{2} \cdot 7^{7} \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1$	$1$		$0$	$3072$	$0.695220$	$4956477625/52983$	$0.86867$	$4.06802$	$[1, 0, 1, -1741, -27835]$	\(y^2+xy+y=x^3-1741x-27835\)	2.3.0.a.1, 28.6.0.a.1, 348.6.0.?, 2436.12.0.?	$[]$
4263.e2	4263e1	4263.e	4263e	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( - 3 \cdot 7^{8} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1$	$4$	$2$	$1$	$1536$	$0.348647$	$-15625/4263$	$0.95144$	$3.28917$	$[1, 0, 1, -26, -1081]$	\(y^2+xy+y=x^3-26x-1081\)	2.3.0.a.1, 28.6.0.b.1, 174.6.0.?, 2436.12.0.?	$[]$
4263.f1	4263f2	4263.f	4263f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{6} \cdot 7^{9} \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1$	$1$		$0$	$8064$	$1.260717$	$1121622319/613089$	$0.94499$	$4.58871$	$[1, 0, 1, -7425, -58607]$	\(y^2+xy+y=x^3-7425x-58607\)	2.3.0.a.1, 28.6.0.a.1, 348.6.0.?, 2436.12.0.?	$[]$
4263.f2	4263f1	4263.f	4263f	$2$	$2$	\( 3 \cdot 7^{2} \cdot 29 \)	\( 3^{3} \cdot 7^{9} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2436$	$12$	$0$	$1$	$4$	$2$	$1$	$4032$	$0.914145$	$510082399/783$	$0.94444$	$4.49444$	$[1, 0, 1, -5710, -166309]$	\(y^2+xy+y=x^3-5710x-166309\)	2.3.0.a.1, 28.6.0.b.1, 348.6.0.?, 1218.6.0.?, 2436.12.0.?	$[]$
4263.g1	4263b1	4263.g	4263b	$1$	$1$	\( 3 \cdot 7^{2} \cdot 29 \)	\( - 3^{3} \cdot 7^{4} \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$2520$	$0.163998$	$-200704/22707$	$0.96810$	$3.02401$	$[0, -1, 1, -16, -351]$	\(y^2+y=x^3-x^2-16x-351\)	6.2.0.a.1	$[]$
4263.h1	4263h1	4263.h	4263h	$1$	$1$	\( 3 \cdot 7^{2} \cdot 29 \)	\( - 3^{3} \cdot 7^{10} \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$1$	$1$		$0$	$17640$	$1.136953$	$-200704/22707$	$0.96810$	$4.42098$	$[0, 1, 1, -800, 121895]$	\(y^2+y=x^3+x^2-800x+121895\)	6.2.0.a.1	$[]$