Elliptic curves over $\Q$ of conductor 144

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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
144.a1	144a4	144.a	144a	$4$	$6$	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$24$	$0.080464$	$54000$	$1.02720$	$5.29787$	$[0, 0, 0, -135, 594]$	\(y^2=x^3-135x+594\)		$[]$
144.a2	144a2	144.a	144a	$4$	$6$	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-12$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$8$	$-0.468842$	$54000$	$1.02720$	$3.97153$	$[0, 0, 0, -15, -22]$	\(y^2=x^3-15x-22\)		$[]$
144.a3	144a1	144.a	144a	$4$	$6$	\( 2^{4} \cdot 3^{2} \)	\( - 2^{4} \cdot 3^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.83	2B				$1$	$1$		$1$	$4$	$-0.815415$	$0$		$2.72106$	$[0, 0, 0, 0, -1]$	\(y^2=x^3-1\)		$[]$
144.a4	144a3	144.a	144a	$4$	$6$	\( 2^{4} \cdot 3^{2} \)	\( - 2^{4} \cdot 3^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.83	2B				$1$	$1$		$1$	$12$	$-0.266109$	$0$		$4.04740$	$[0, 0, 0, 0, 27]$	\(y^2=x^3+27\)		$[]$
144.b1	144b5	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( 2^{11} \cdot 3^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.270	2B	$48$	$192$	$1$	$1$	$1$		$1$	$64$	$0.597101$	$3065617154/9$	$1.21059$	$7.25577$	$[0, 0, 0, -3459, -78302]$	\(y^2=x^3-3459x-78302\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.r.1.3, 12.12.0-4.c.1.2, 16.96.0-16.l.1.7, $\ldots$	$[]$
144.b2	144b4	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( 2^{10} \cdot 3^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.126	2B	$48$	$192$	$1$	$1$	$1$		$3$	$32$	$0.250527$	$28756228/3$	$1.05617$	$6.17679$	$[0, 0, 0, -579, 5362]$	\(y^2=x^3-579x+5362\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.5, 12.24.0-12.h.1.2, 16.96.0-16.bb.2.5, $\ldots$	$[]$
144.b3	144b3	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( 2^{10} \cdot 3^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.137	2Cs	$24$	$192$	$1$	$1$	$1$		$3$	$32$	$0.250527$	$1556068/81$	$1.03212$	$5.58991$	$[0, 0, 0, -219, -1190]$	\(y^2=x^3-219x-1190\)	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.e.2.3, 12.24.0-4.b.1.3, 24.192.1-24.bl.2.3	$[]$
144.b4	144b2	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.21	2Cs	$24$	$192$	$1$	$1$	$1$		$3$	$16$	$-0.096046$	$35152/9$	$0.97255$	$4.54832$	$[0, 0, 0, -39, 70]$	\(y^2=x^3-39x+70\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.96.0-8.h.1.3, 12.48.0-12.c.1.2, 24.192.1-24.bu.1.8	$[]$
144.b5	144b1	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( - 2^{4} \cdot 3^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.162	2B	$48$	$192$	$1$	$1$	$1$		$1$	$8$	$-0.442620$	$2048/3$	$1.17572$	$3.50415$	$[0, 0, 0, 6, 7]$	\(y^2=x^3+6x+7\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.ba.1.8, 12.24.0-12.g.1.1, $\ldots$	$[]$
144.b6	144b6	144.b	144b	$6$	$8$	\( 2^{4} \cdot 3^{2} \)	\( - 2^{11} \cdot 3^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.251	2B	$48$	$192$	$1$	$1$	$1$		$1$	$64$	$0.597101$	$207646/6561$	$1.15980$	$6.12527$	$[0, 0, 0, 141, -4718]$	\(y^2=x^3+141x-4718\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 12.12.0-4.c.1.2, 16.96.0-8.m.1.2, $\ldots$	$[]$

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