Elliptic curves over $\Q$ of conductor 847

Results (6 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
847.a1	847c2	847.a	847c	$2$	$2$	\( 7 \cdot 11^{2} \)	\( 7^{6} \cdot 11^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.591964351$	$1$		$6$	$1440$	$1.112928$	$15124197817/1294139$	$[1, 1, 1, -6234, -177484]$	\(y^2+xy+y=x^3+x^2-6234x-177484\)
847.a2	847c1	847.a	847c	$2$	$2$	\( 7 \cdot 11^{2} \)	\( - 7^{3} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.183928702$	$1$		$3$	$720$	$0.766355$	$4657463/41503$	$[1, 1, 1, 421, -12440]$	\(y^2+xy+y=x^3+x^2+421x-12440\)
847.b1	847b1	847.b	847b	$1$	$1$	\( 7 \cdot 11^{2} \)	\( - 7^{2} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.175784754$	$1$		$6$	$480$	$0.412294$	$884736/539$	$[0, 0, 1, 242, -333]$	\(y^2+y=x^3+242x-333\)
847.c1	847a1	847.c	847a	$3$	$9$	\( 7 \cdot 11^{2} \)	\( - 7^{2} \cdot 11^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$800$	$0.903948$	$-78843215872/539$	$[0, 1, 1, -10809, -436166]$	\(y^2+y=x^3+x^2-10809x-436166\)
847.c2	847a2	847.c	847a	$3$	$9$	\( 7 \cdot 11^{2} \)	\( - 7^{6} \cdot 11^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$2400$	$1.453255$	$-13278380032/156590819$	$[0, 1, 1, -5969, -822761]$	\(y^2+y=x^3+x^2-5969x-822761\)
847.c3	847a3	847.c	847a	$3$	$9$	\( 7 \cdot 11^{2} \)	\( - 7^{2} \cdot 11^{15} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$7200$	$2.002560$	$9463555063808/115539436859$	$[0, 1, 1, 53321, 21262764]$	\(y^2+y=x^3+x^2+53321x+21262764\)