Elliptic curves over $\Q$ of conductor 441

Results (18 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
441.a1	441f2	441.a	441f	$2$	$13$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{19} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.2	13B.4.2	$0.991510447$	$1$		$4$	$624$	$0.986693$	$-1713910976512/1594323$	$[0, 0, 1, -8211, -286610]$	\(y^2+y=x^3-8211x-286610\)
441.a2	441f1	441.a	441f	$2$	$13$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{7} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.1	13B.4.1	$0.076270034$	$1$		$10$	$48$	$-0.295781$	$-28672/3$	$[0, 0, 1, -21, 40]$	\(y^2+y=x^3-21x+40\)
441.b1	441e2	441.b	441e	$2$	$13$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{19} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.2	13B.4.2	$1$	$1$		$0$	$4368$	$1.959648$	$-1713910976512/1594323$	$[0, 0, 1, -402339, 98307144]$	\(y^2+y=x^3-402339x+98307144\)
441.b2	441e1	441.b	441e	$2$	$13$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{7} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$13$	13.28.0.1	13B.4.1	$1$	$1$		$0$	$336$	$0.677174$	$-28672/3$	$[0, 0, 1, -1029, -13806]$	\(y^2+y=x^3-1029x-13806\)
441.c1	441d4	441.c	441d	$4$	$14$	\( 3^{2} \cdot 7^{2} \)	\( 3^{6} \cdot 7^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$		✓				$1.534261868$	$1$		$6$	$448$	$1.069696$	$16581375$	$[1, -1, 1, -16400, -804212]$	\(y^2+xy+y=x^3-x^2-16400x-804212\)
441.c2	441d3	441.c	441d	$4$	$14$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{6} \cdot 7^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$		✓				$3.068523736$	$1$		$5$	$224$	$0.723123$	$-3375$	$[1, -1, 1, -965, -13940]$	\(y^2+xy+y=x^3-x^2-965x-13940\)
441.c3	441d2	441.c	441d	$4$	$14$	\( 3^{2} \cdot 7^{2} \)	\( 3^{6} \cdot 7^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$		✓				$0.219180266$	$1$		$12$	$64$	$0.096741$	$16581375$	$[1, -1, 1, -335, 2440]$	\(y^2+xy+y=x^3-x^2-335x+2440\)
441.c4	441d1	441.c	441d	$4$	$14$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{6} \cdot 7^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$		✓				$0.438360533$	$1$		$7$	$32$	$-0.249832$	$-3375$	$[1, -1, 1, -20, 46]$	\(y^2+xy+y=x^3-x^2-20x+46\)
441.d1	441b2	441.d	441b	$2$	$3$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{9} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3, 7$	27.648.18.4, 7.84.1.1	3B.1.2, 7Ns.6.1.2	$0.298091926$	$1$		$6$	$72$	$0.151479$	$0$	$[0, 0, 1, 0, -331]$	\(y^2+y=x^3-331\)
441.d2	441b1	441.d	441b	$2$	$3$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{3} \cdot 7^{4} \)	$1$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3, 7$	27.648.18.1, 7.84.1.1	3B.1.1, 7Ns.6.1.2	$0.894275780$	$1$		$6$	$24$	$-0.397828$	$0$	$[0, 0, 1, 0, 12]$	\(y^2+y=x^3+12\)
441.e1	441a1	441.e	441a	$2$	$3$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{3} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$7$	7.84.1.1	7Ns.6.1.2	$1$	$1$		$0$	$168$	$0.575128$	$0$	$[0, 0, 1, 0, -4202]$	\(y^2+y=x^3-4202\)
441.e2	441a2	441.e	441a	$2$	$3$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{9} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$7$	7.84.1.1	7Ns.6.1.2	$1$	$1$		$0$	$504$	$1.124434$	$0$	$[0, 0, 1, 0, 113447]$	\(y^2+y=x^3+113447\)
441.f1	441c5	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( 3^{7} \cdot 7^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.119	2B	$10.55403529$	$1$		$0$	$1536$	$1.596466$	$53297461115137/147$	$[1, -1, 0, -345753, -78165914]$	\(y^2+xy=x^3-x^2-345753x-78165914\)
441.f2	441c3	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( 3^{8} \cdot 7^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.113	2Cs	$5.277017646$	$1$		$2$	$768$	$1.249893$	$13027640977/21609$	$[1, -1, 0, -21618, -1216265]$	\(y^2+xy=x^3-x^2-21618x-1216265\)
441.f3	441c4	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( 3^{14} \cdot 7^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.99	2B	$1.319254411$	$1$		$4$	$768$	$1.249893$	$6570725617/45927$	$[1, -1, 0, -17208, 867901]$	\(y^2+xy=x^3-x^2-17208x+867901\)
441.f4	441c6	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{7} \cdot 7^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.131	2B	$2.638508823$	$1$		$2$	$1536$	$1.596466$	$-4354703137/17294403$	$[1, -1, 0, -15003, -1979636]$	\(y^2+xy=x^3-x^2-15003x-1979636\)
441.f5	441c2	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( 3^{10} \cdot 7^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.65	2Cs	$2.638508823$	$1$		$6$	$384$	$0.903319$	$7189057/3969$	$[1, -1, 0, -1773, -5720]$	\(y^2+xy=x^3-x^2-1773x-5720\)
441.f6	441c1	441.f	441c	$6$	$8$	\( 3^{2} \cdot 7^{2} \)	\( - 3^{8} \cdot 7^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.85	2B	$1.319254411$	$1$		$5$	$192$	$0.556746$	$103823/63$	$[1, -1, 0, 432, -869]$	\(y^2+xy=x^3-x^2+432x-869\)