Elliptic curves over $\Q$ of conductor 288

Results (16 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
288.a1	288a2	288.a	288a	$2$	$2$	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$0.250591196$	$1$		$11$	$32$	$-0.342733$	$1728$		$3.36720$	$[0, 0, 0, -12, 0]$	\(y^2=x^3-12x\)		$[(-2, 4)]$
288.a2	288a1	288.a	288a	$2$	$2$	\( 2^{5} \cdot 3^{2} \)	\( - 2^{6} \cdot 3^{3} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$0.501182392$	$1$		$7$	$16$	$-0.689306$	$1728$		$2.63280$	$[0, 0, 0, 3, 0]$	\(y^2=x^3+3x\)		$[(1, 2)]$
288.b1	288b2	288.b	288b	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{9} \cdot 3^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.64	2B	$24$	$48$	$0$	$2.480678691$	$1$		$3$	$64$	$0.123086$	$7301384/3$	$1.03749$	$5.05629$	$[0, 0, 0, -291, -1910]$	\(y^2=x^3-291x-1910\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 24.48.0-24.bi.1.8	$[(26, 90)]$
288.b2	288b3	288.b	288b	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.54	2B	$24$	$48$	$0$	$0.620169672$	$1$		$15$	$64$	$0.123086$	$140608/3$	$1.02705$	$4.72600$	$[0, 0, 0, -156, 736]$	\(y^2=x^3-156x+736\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 12.24.0-12.h.1.2, 24.48.0-24.bk.1.5	$[(5, 9)]$
288.b3	288b1	288.b	288b	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.6	2Cs	$24$	$48$	$0$	$1.240339345$	$1$		$9$	$32$	$-0.223488$	$21952/9$	$1.09175$	$3.66366$	$[0, 0, 0, -21, -20]$	\(y^2=x^3-21x-20\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 12.24.0-12.a.1.1, 24.48.0-24.f.1.4	$[(-3, 4)]$
288.b4	288b4	288.b	288b	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( - 2^{9} \cdot 3^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.106	2B	$24$	$48$	$0$	$0.620169672$	$1$		$9$	$64$	$0.123086$	$97336/81$	$1.05989$	$4.29385$	$[0, 0, 0, 69, -146]$	\(y^2=x^3+69x-146\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 12.12.0-4.c.1.2, 24.48.0-24.n.1.6	$[(5, 18)]$
288.c1	288c3	288.c	288c	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{9} \cdot 3^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.54	2B	$24$	$48$	$0$	$1$	$1$		$3$	$64$	$0.123086$	$7301384/3$	$1.03749$	$5.05629$	$[0, 0, 0, -291, 1910]$	\(y^2=x^3-291x+1910\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 24.48.0-24.bi.1.7	$[]$
288.c2	288c2	288.c	288c	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.64	2B	$24$	$48$	$0$	$1$	$1$		$1$	$64$	$0.123086$	$140608/3$	$1.02705$	$4.72600$	$[0, 0, 0, -156, -736]$	\(y^2=x^3-156x-736\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 12.24.0-12.h.1.1, 24.48.0-24.bk.1.8	$[]$
288.c3	288c1	288.c	288c	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.6	2Cs	$24$	$48$	$0$	$1$	$1$		$3$	$32$	$-0.223488$	$21952/9$	$1.09175$	$3.66366$	$[0, 0, 0, -21, 20]$	\(y^2=x^3-21x+20\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 12.24.0-12.a.1.2, 24.48.0-24.f.1.1	$[]$
288.c4	288c4	288.c	288c	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( - 2^{9} \cdot 3^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.106	2B	$24$	$48$	$0$	$1$	$1$		$1$	$64$	$0.123086$	$97336/81$	$1.05989$	$4.29385$	$[0, 0, 0, 69, 146]$	\(y^2=x^3+69x+146\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 12.12.0-4.c.1.1, 24.48.0-24.n.1.8	$[]$
288.d1	288d2	288.d	288d	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{9} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$32$	$-0.068080$	$287496$	$1.17246$	$4.48510$	$[0, 0, 0, -99, -378]$	\(y^2=x^3-99x-378\)		$[]$
288.d2	288d3	288.d	288d	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{9} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$32$	$-0.068080$	$287496$	$1.17246$	$4.48510$	$[0, 0, 0, -99, 378]$	\(y^2=x^3-99x+378\)		$[]$
288.d3	288d1	288.d	288d	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.143	2Cs				$1$	$1$		$3$	$16$	$-0.414653$	$1728$		$3.21480$	$[0, 0, 0, -9, 0]$	\(y^2=x^3-9x\)		$[]$
288.d4	288d4	288.d	288d	$4$	$4$	\( 2^{5} \cdot 3^{2} \)	\( - 2^{12} \cdot 3^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.178	2B				$1$	$1$		$1$	$32$	$-0.068080$	$1728$		$3.94920$	$[0, 0, 0, 36, 0]$	\(y^2=x^3+36x\)		$[]$
288.e1	288e2	288.e	288e	$2$	$2$	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$96$	$0.206573$	$1728$		$4.53120$	$[0, 0, 0, -108, 0]$	\(y^2=x^3-108x\)		$[]$
288.e2	288e1	288.e	288e	$2$	$2$	\( 2^{5} \cdot 3^{2} \)	\( - 2^{6} \cdot 3^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$48$	$-0.140000$	$1728$		$3.79680$	$[0, 0, 0, 27, 0]$	\(y^2=x^3+27x\)		$[]$