Elliptic curves over $\Q$ of conductor 63

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
63.a1	63a5	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( 3^{7} \cdot 7^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.38	2B	$1$	$1$		$2$	$32$	$0.623511$	$53297461115137/147$	$[1, -1, 0, -7056, 229905]$	\(y^2+xy=x^3-x^2-7056x+229905\)
63.a2	63a4	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( 3^{8} \cdot 7^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.18	2Cs	$1$	$1$		$2$	$16$	$0.276938$	$13027640977/21609$	$[1, -1, 0, -441, 3672]$	\(y^2+xy=x^3-x^2-441x+3672\)
63.a3	63a3	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( 3^{14} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.98	2B	$1$	$1$		$0$	$16$	$0.276938$	$6570725617/45927$	$[1, -1, 0, -351, -2430]$	\(y^2+xy=x^3-x^2-351x-2430\)
63.a4	63a6	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( - 3^{7} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.183	2B	$1$	$1$		$0$	$32$	$0.623511$	$-4354703137/17294403$	$[1, -1, 0, -306, 5859]$	\(y^2+xy=x^3-x^2-306x+5859\)
63.a5	63a2	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( 3^{10} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.66	2Cs	$1$	$1$		$2$	$8$	$-0.069636$	$7189057/3969$	$[1, -1, 0, -36, 27]$	\(y^2+xy=x^3-x^2-36x+27\)
63.a6	63a1	63.a	63a	$6$	$8$	\( 3^{2} \cdot 7 \)	\( - 3^{8} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.84	2B	$1$	$1$		$1$	$4$	$-0.416209$	$103823/63$	$[1, -1, 0, 9, 0]$	\(y^2+xy=x^3-x^2+9x\)