Elliptic curves over $\Q$ of conductor 546

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
546.a1	546a1	546.a	546a	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2 \cdot 3^{5} \cdot 7^{3} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$120$	$0.018178$	$-141339344329/2167074$	$[1, 1, 0, -108, -486]$	\(y^2+xy=x^3+x^2-108x-486\)
546.b1	546c3	546.b	546c	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{2} \cdot 3^{12} \cdot 7 \cdot 13 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$0.615546328$	$1$		$14$	$384$	$0.580644$	$828279937799497/193444524$	$[1, 0, 1, -1957, 33140]$	\(y^2+xy+y=x^3-1957x+33140\)
546.b2	546c2	546.b	546c	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$0.307773164$	$1$		$18$	$192$	$0.234070$	$281397674377/96589584$	$[1, 0, 1, -137, 380]$	\(y^2+xy+y=x^3-137x+380\)
546.b3	546c1	546.b	546c	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{8} \cdot 3^{3} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$0.615546328$	$1$		$7$	$96$	$-0.112504$	$19968681097/628992$	$[1, 0, 1, -57, -164]$	\(y^2+xy+y=x^3-57x-164\)
546.b4	546c4	546.b	546c	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{2} \cdot 3^{3} \cdot 7^{4} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$0.153886582$	$1$		$14$	$384$	$0.580644$	$7264187703863/7406095788$	$[1, 0, 1, 403, 2756]$	\(y^2+xy+y=x^3+403x+2756\)
546.c1	546b1	546.c	546b	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{5} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$40$	$-0.519256$	$-47045881/8736$	$[1, 0, 1, -8, -10]$	\(y^2+xy+y=x^3-8x-10\)
546.d1	546d3	546.d	546d	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{27} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.3	3B.1.2	$1$	$9$	$3$	$0$	$1944$	$1.151459$	$-1956469094246217097/36641439744$	$[1, 0, 1, -26057, -1621108]$	\(y^2+xy+y=x^3-26057x-1621108\)
546.d2	546d2	546.d	546d	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{9} \cdot 3^{3} \cdot 7^{3} \cdot 13^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.24.0.1	3Cs.1.1	$1$	$1$		$2$	$648$	$0.602153$	$-198461344537/10417365504$	$[1, 0, 1, -122, -4948]$	\(y^2+xy+y=x^3-122x-4948\)
546.d3	546d1	546.d	546d	$3$	$9$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{9} \cdot 7 \cdot 13 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.1	3B.1.1	$1$	$1$		$2$	$216$	$0.052847$	$270840023/14329224$	$[1, 0, 1, 13, 182]$	\(y^2+xy+y=x^3+13x+182\)
546.e1	546e1	546.e	546e	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{17} \cdot 3^{7} \cdot 7 \cdot 13^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1$	$1$		$0$	$4760$	$1.689280$	$-112205650221491190337/745029571313664$	$[1, 1, 1, -100484, -12372091]$	\(y^2+xy+y=x^3+x^2-100484x-12372091\)
546.f1	546f2	546.f	546f	$2$	$7$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2 \cdot 3 \cdot 7 \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$1$	$49$	$7$	$0$	$8232$	$2.046547$	$-5486773802537974663600129/2635437714$	$[1, 0, 0, -3674496, -2711401518]$	\(y^2+xy=x^3-3674496x-2711401518\)
546.f2	546f1	546.f	546f	$2$	$7$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2^{7} \cdot 3^{7} \cdot 7^{7} \cdot 13 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$1$	$1$		$6$	$1176$	$1.073593$	$40251338884511/2997011332224$	$[1, 0, 0, 714, -82908]$	\(y^2+xy=x^3+714x-82908\)
546.g1	546g3	546.g	546g	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2 \cdot 3 \cdot 7^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$1$	$1$		$0$	$192$	$0.123973$	$8020417344913/187278$	$[1, 0, 0, -417, 3243]$	\(y^2+xy=x^3-417x+3243\)
546.g2	546g2	546.g	546g	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$1$	$1$		$2$	$96$	$-0.222601$	$2181825073/298116$	$[1, 0, 0, -27, 45]$	\(y^2+xy=x^3-27x+45\)
546.g3	546g1	546.g	546g	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$1$	$1$		$1$	$48$	$-0.569175$	$38272753/4368$	$[1, 0, 0, -7, -7]$	\(y^2+xy=x^3-7x-7\)
546.g4	546g4	546.g	546g	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( - 2 \cdot 3^{4} \cdot 7 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$1$	$1$		$0$	$192$	$0.123973$	$8780064047/32388174$	$[1, 0, 0, 43, 255]$	\(y^2+xy=x^3+43x+255\)