Elliptic curves over $\Q$ of conductor 648

Results (4 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
648.a1	648b1	648.a	648b	$1$	$1$	\( 2^{3} \cdot 3^{4} \)	\( 2^{4} \cdot 3^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.2	2Cn	$36$	$12$	$0$	$0.264279496$	$1$		$4$	$24$	$-0.706588$	$2304$	$0.77371$	$2.30301$	$[0, 0, 0, -3, -1]$	\(y^2=x^3-3x-1\)	2.2.0.a.1, 4.4.0-2.a.1.1, 18.6.0.a.1, 36.12.0-18.a.1.3	$[(-1, 1)]$
648.b1	648a1	648.b	648a	$1$	$1$	\( 2^{3} \cdot 3^{4} \)	\( - 2^{10} \cdot 3^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	4.16.0.2, 5.5.0.1	5S4	$20$	$80$	$2$	$0.354524139$	$1$		$4$	$48$	$-0.375659$	$-36$	$1.04124$	$2.90417$	$[0, 0, 0, -3, 14]$	\(y^2=x^3-3x+14\)	4.16.0-4.b.1.1, 5.5.0.a.1, 20.80.2-20.b.1.2	$[(-1, 4)]$
648.c1	648d1	648.c	648d	$1$	$1$	\( 2^{3} \cdot 3^{4} \)	\( 2^{4} \cdot 3^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	2.2.0.1	2Cn	$36$	$12$	$0$	$0.138020204$	$1$		$8$	$72$	$-0.157282$	$2304$	$0.77371$	$3.32120$	$[0, 0, 0, -27, 27]$	\(y^2=x^3-27x+27\)	2.2.0.a.1, 12.4.0-2.a.1.1, 18.6.0.a.1, 36.12.0-18.a.1.1	$[(-3, 9)]$
648.d1	648c1	648.d	648c	$1$	$1$	\( 2^{3} \cdot 3^{4} \)	\( - 2^{10} \cdot 3^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	4.8.0.2, 5.5.0.1	5S4	$60$	$80$	$2$	$1$	$1$		$0$	$144$	$0.173646$	$-36$	$1.04124$	$3.92236$	$[0, 0, 0, -27, -378]$	\(y^2=x^3-27x-378\)	4.8.0.b.1, 5.5.0.a.1, 12.16.0-4.b.1.1, 20.40.2.b.1, 60.80.2-20.b.1.1	$[]$