Elliptic curves over $\Q$ of conductor 168

Results (8 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
168.a1	168b4	168.a	168b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{10} \cdot 3^{3} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$168$	$48$	$0$	$1$	$1$		$1$	$96$	$0.528189$	$7080974546692/189$	$1.03534$	$7.12728$	$[0, -1, 0, -4032, 99900]$	\(y^2=x^3-x^2-4032x+99900\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.z.1.12, $\ldots$	$[]$
168.a2	168b3	168.a	168b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{10} \cdot 3^{12} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$168$	$48$	$0$	$1$	$1$		$1$	$96$	$0.528189$	$6522128932/3720087$	$1.09944$	$5.76310$	$[0, -1, 0, -392, -228]$	\(y^2=x^3-x^2-392x-228\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.z.1.16, 28.24.0-28.h.1.1, 168.48.0.?	$[]$
168.a3	168b2	168.a	168b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{8} \cdot 3^{6} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$84$	$48$	$0$	$1$	$1$		$3$	$48$	$0.181615$	$6940769488/35721$	$0.97939$	$5.50469$	$[0, -1, 0, -252, 1620]$	\(y^2=x^3-x^2-252x+1620\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.1, 28.24.0-28.a.1.2, 84.48.0.?	$[]$
168.a4	168b1	168.a	168b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( - 2^{4} \cdot 3^{3} \cdot 7^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$168$	$48$	$0$	$1$	$1$		$3$	$24$	$-0.164958$	$-2725888/64827$	$1.07980$	$4.16295$	$[0, -1, 0, -7, 52]$	\(y^2=x^3-x^2-7x+52\)	2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 12.24.0-12.g.1.2, 56.24.0-56.ba.1.4, $\ldots$	$[]$
168.b1	168a3	168.b	168a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{10} \cdot 3^{4} \cdot 7 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$168$	$48$	$0$	$1$	$1$		$3$	$32$	$0.006959$	$381775972/567$	$0.96461$	$5.20921$	$[0, 1, 0, -152, 672]$	\(y^2=x^3+x^2-152x+672\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 28.24.0-28.h.1.2, 168.48.0.?	$[]$
168.b2	168a2	168.b	168a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$84$	$48$	$0$	$1$	$1$		$3$	$16$	$-0.339614$	$810448/441$	$0.95393$	$3.73744$	$[0, 1, 0, -12, 0]$	\(y^2=x^3+x^2-12x\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 28.24.0-28.a.1.1, 84.48.0.?	$[]$
168.b3	168a1	168.b	168a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( 2^{4} \cdot 3 \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$168$	$48$	$0$	$1$	$1$		$1$	$8$	$-0.686188$	$2725888/21$	$0.93026$	$3.43306$	$[0, 1, 0, -7, -10]$	\(y^2=x^3+x^2-7x-10\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$	$[]$
168.b4	168a4	168.b	168a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \)	\( - 2^{10} \cdot 3 \cdot 7^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$168$	$48$	$0$	$1$	$1$		$1$	$32$	$0.006959$	$11696828/7203$	$1.01215$	$4.52897$	$[0, 1, 0, 48, 48]$	\(y^2=x^3+x^2+48x+48\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 56.24.0-56.ba.1.12, $\ldots$	$[]$