Elliptic curves over $\Q$ of conductor 300042

Results (15 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
300042.a1	300042a1	300042.a	300042a	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{6} \cdot 3^{6} \cdot 79 \cdot 211^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1.187946611$	$1$		$4$	$305280$	$0.855130$	$689167345537/225098176$	$0.86769$	$2.68405$	$[1, -1, 0, -1656, 17536]$	\(y^2+xy=x^3-x^2-1656x+17536\)	316.2.0.?	$[(39, 86)]$
300042.b1	300042b1	300042.b	300042b	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2 \cdot 3^{3} \cdot 79 \cdot 211 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$2.064468861$	$1$		$6$	$43520$	$-0.024434$	$4767078987/33338$	$0.72387$	$2.02835$	$[1, -1, 0, -105, 439]$	\(y^2+xy=x^3-x^2-105x+439\)	400056.2.0.?	$[(5, 2), (23/2, -17/2)]$
300042.c1	300042c1	300042.c	300042c	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{13} \cdot 3^{13} \cdot 79 \cdot 211 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$5.480546299$	$1$		$2$	$1188096$	$1.460737$	$1171205436932929/298640203776$	$0.86447$	$3.27383$	$[1, -1, 0, -19764, 804816]$	\(y^2+xy=x^3-x^2-19764x+804816\)	400056.2.0.?	$[(211, 2343)]$
300042.d1	300042d1	300042.d	300042d	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{6} \cdot 3^{6} \cdot 79 \cdot 211^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1$	$1$		$0$	$426240$	$0.857990$	$770842973809/225098176$	$0.80571$	$2.69293$	$[1, -1, 0, -1719, 19741]$	\(y^2+xy=x^3-x^2-1719x+19741\)	316.2.0.?	$[]$
300042.e1	300042e2	300042.e	300042e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{2} \cdot 3^{12} \cdot 79 \cdot 211^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$200028$	$12$	$0$	$2.660868549$	$1$		$2$	$589824$	$1.270714$	$649304417969857/10256035644$	$0.85435$	$3.22706$	$[1, -1, 0, -16236, 789412]$	\(y^2+xy=x^3-x^2-16236x+789412\)	2.3.0.a.1, 316.6.0.?, 2532.6.0.?, 200028.12.0.?	$[(62, 104)]$
300042.e2	300042e1	300042.e	300042e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{4} \cdot 3^{9} \cdot 79^{2} \cdot 211 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$200028$	$12$	$0$	$5.321737098$	$1$		$1$	$294912$	$0.924140$	$1243337227777/568879632$	$0.82057$	$2.73084$	$[1, -1, 0, -2016, -15440]$	\(y^2+xy=x^3-x^2-2016x-15440\)	2.3.0.a.1, 316.6.0.?, 1266.6.0.?, 200028.12.0.?	$[(1615/3, 60185/3)]$
300042.f1	300042f1	300042.f	300042f	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( - 2^{4} \cdot 3^{12} \cdot 79 \cdot 211 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$66676$	$2$	$0$	$6.286003614$	$1$		$0$	$397824$	$0.868366$	$-1243337227777/194427216$	$0.80620$	$2.74981$	$[1, -1, 0, -2016, -38768]$	\(y^2+xy=x^3-x^2-2016x-38768\)	66676.2.0.?	$[(2564/5, 107152/5)]$
300042.g1	300042g1	300042.g	300042g	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{5} \cdot 3^{7} \cdot 79 \cdot 211 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$3.477292333$	$1$		$6$	$206080$	$0.551622$	$135559106353/1600224$	$0.77998$	$2.55512$	$[1, -1, 0, -963, -11147]$	\(y^2+xy=x^3-x^2-963x-11147\)	400056.2.0.?	$[(-19, 5), (41, 110)]$
300042.h1	300042h2	300042.h	300042h	$2$	$3$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2 \cdot 3^{11} \cdot 79^{3} \cdot 211^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$400056$	$16$	$0$	$1$	$4$	$2$	$2$	$9711360$	$2.270714$	$72918170522696196433/2250945132306174$	$0.92211$	$4.14913$	$[1, -1, 0, -783333, 259831503]$	\(y^2+xy=x^3-x^2-783333x+259831503\)	3.8.0-3.a.1.2, 400056.16.0.?	$[]$
300042.h2	300042h1	300042.h	300042h	$2$	$3$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{3} \cdot 3^{21} \cdot 79 \cdot 211 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$400056$	$16$	$0$	$1$	$4$	$2$	$0$	$3237120$	$1.721407$	$177444640175483953/1913455446264$	$0.89050$	$3.67192$	$[1, -1, 0, -105363, -13014243]$	\(y^2+xy=x^3-x^2-105363x-13014243\)	3.8.0-3.a.1.1, 400056.16.0.?	$[]$
300042.i1	300042i1	300042.i	300042i	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{3} \cdot 3^{9} \cdot 79^{5} \cdot 211 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$1$	$4$	$2$	$0$	$5333760$	$1.973251$	$20261349184552659/5194071201512$	$0.91177$	$3.76120$	$[1, -1, 0, -153348, -17212168]$	\(y^2+xy=x^3-x^2-153348x-17212168\)	400056.2.0.?	$[]$
300042.j1	300042j1	300042.j	300042j	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{3} \cdot 3^{3} \cdot 79^{5} \cdot 211 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$4.371874867$	$1$		$2$	$1777920$	$1.423946$	$20261349184552659/5194071201512$	$0.91177$	$3.23853$	$[1, -1, 1, -17039, 643167]$	\(y^2+xy+y=x^3-x^2-17039x+643167\)	400056.2.0.?	$[(105, 6)]$
300042.k1	300042k1	300042.k	300042k	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2^{12} \cdot 3^{6} \cdot 79 \cdot 211^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1.287305674$	$1$		$4$	$887040$	$1.304766$	$1057498103580841/14406283264$	$0.85779$	$3.26573$	$[1, -1, 1, -19103, -999417]$	\(y^2+xy+y=x^3-x^2-19103x-999417\)	316.2.0.?	$[(171, 758)]$
300042.l1	300042l1	300042.l	300042l	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( 2 \cdot 3^{9} \cdot 79 \cdot 211 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$400056$	$2$	$0$	$9.759259625$	$1$		$0$	$130560$	$0.524873$	$4767078987/33338$	$0.72387$	$2.55101$	$[1, -1, 1, -947, -10907]$	\(y^2+xy+y=x^3-x^2-947x-10907\)	400056.2.0.?	$[(11647/18, 29287/18)]$
300042.m1	300042m1	300042.m	300042m	$1$	$1$	\( 2 \cdot 3^{2} \cdot 79 \cdot 211 \)	\( - 2^{32} \cdot 3^{8} \cdot 79 \cdot 211 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$66676$	$2$	$0$	$1$	$1$		$0$	$4165632$	$2.079407$	$916763542913931623/644335288713216$	$0.95307$	$3.80213$	$[1, -1, 1, 182146, -13903347]$	\(y^2+xy+y=x^3-x^2+182146x-13903347\)	66676.2.0.?	$[]$