Elliptic curves over $\Q$ of conductor 30899

Results (10 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
30899.a1	30899d1	30899.a	30899d	$1$	$1$	\( 11 \cdot 53^{2} \)	\( - 11^{3} \cdot 53^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$3504384$	$2.595932$	$13090860306432/10502230211$	$0.97746$	$5.22559$	$[0, 0, 1, 1379219, -387489612]$	\(y^2+y=x^3+1379219x-387489612\)	22.2.0.a.1	$[]$
30899.b1	30899a1	30899.b	30899a	$1$	$1$	\( 11 \cdot 53^{2} \)	\( - 11 \cdot 53^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1.558107936$	$1$		$4$	$134784$	$1.531998$	$20123648/30899$	$0.77583$	$3.97949$	$[0, -1, 1, 15918, -999198]$	\(y^2+y=x^3-x^2+15918x-999198\)	22.2.0.a.1	$[(1767, 74438)]$
30899.c1	30899f2	30899.c	30899f	$2$	$2$	\( 11 \cdot 53^{2} \)	\( 11^{2} \cdot 53^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2332$	$12$	$0$	$17.55514568$	$1$		$0$	$463008$	$2.203728$	$14706125/121$	$0.91816$	$5.05262$	$[1, 0, 0, -759893, -253207124]$	\(y^2+xy=x^3-759893x-253207124\)	2.3.0.a.1, 44.6.0.d.1, 106.6.0.?, 2332.12.0.?	$[(-229053507/653, 9117050912/653)]$
30899.c2	30899f1	30899.c	30899f	$2$	$2$	\( 11 \cdot 53^{2} \)	\( - 11 \cdot 53^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2332$	$12$	$0$	$35.11029136$	$1$		$1$	$231504$	$1.857153$	$-125/11$	$0.77547$	$4.40991$	$[1, 0, 0, -15508, -9197721]$	\(y^2+xy=x^3-15508x-9197721\)	2.3.0.a.1, 44.6.0.d.1, 212.6.0.?, 1166.6.0.?, 2332.12.0.?	$[(1079622225609355/2134657, 5313793199950384385454/2134657)]$
30899.d1	30899b1	30899.d	30899b	$1$	$1$	\( 11 \cdot 53^{2} \)	\( - 11^{4} \cdot 53^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$212$	$2$	$0$	$1$	$1$		$0$	$1078272$	$2.484631$	$-5096439860329/2179708157$	$0.95523$	$5.18787$	$[1, 0, 0, -1007085, -513067714]$	\(y^2+xy=x^3-1007085x-513067714\)	212.2.0.?	$[]$
30899.e1	30899e2	30899.e	30899e	$2$	$2$	\( 11 \cdot 53^{2} \)	\( 11^{2} \cdot 53^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2332$	$12$	$0$	$9.234255903$	$1$		$0$	$8736$	$0.218580$	$14706125/121$	$0.91816$	$2.74844$	$[1, 1, 0, -270, -1813]$	\(y^2+xy=x^3+x^2-270x-1813\)	2.3.0.a.1, 44.6.0.d.1, 106.6.0.?, 2332.12.0.?	$[(74078/7, 19909877/7)]$
30899.e2	30899e1	30899.e	30899e	$2$	$2$	\( 11 \cdot 53^{2} \)	\( - 11 \cdot 53^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2332$	$12$	$0$	$18.46851180$	$1$		$1$	$4368$	$-0.127994$	$-125/11$	$0.77547$	$2.10573$	$[1, 1, 0, -5, -64]$	\(y^2+xy=x^3+x^2-5x-64\)	2.3.0.a.1, 44.6.0.d.1, 212.6.0.?, 1166.6.0.?, 2332.12.0.?	$[(104084404/525, 1036302114658/525)]$
30899.f1	30899c3	30899.f	30899c	$3$	$25$	\( 11 \cdot 53^{2} \)	\( - 11 \cdot 53^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$29150$	$1200$	$37$	$1$	$25$	$5$	$0$	$748800$	$2.481853$	$-52893159101157376/11$	$1.09296$	$6.02882$	$[0, 1, 1, -21967316, -39636368621]$	\(y^2+y=x^3+x^2-21967316x-39636368621\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 265.24.0.?, $\ldots$	$[]$
30899.f2	30899c2	30899.f	30899c	$3$	$25$	\( 11 \cdot 53^{2} \)	\( - 11^{5} \cdot 53^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$29150$	$1200$	$37$	$1$	$1$		$0$	$149760$	$1.677135$	$-122023936/161051$	$1.01300$	$4.22011$	$[0, 1, 1, -29026, -3457281]$	\(y^2+y=x^3+x^2-29026x-3457281\)	5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 265.120.0.?, 275.300.12.?, $\ldots$	$[]$
30899.f3	30899c1	30899.f	30899c	$3$	$25$	\( 11 \cdot 53^{2} \)	\( - 11 \cdot 53^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$29150$	$1200$	$37$	$1$	$1$		$0$	$29952$	$0.872417$	$-4096/11$	$0.82546$	$3.27606$	$[0, 1, 1, -936, 25879]$	\(y^2+y=x^3+x^2-936x+25879\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 265.24.0.?, $\ldots$	$[]$