Elliptic curves over $\Q$ of conductor 35131

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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
35131.a1	35131e1	35131.a	35131e	$1$	$1$	\( 19 \cdot 43^{2} \)	\( - 19^{3} \cdot 43^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$11.80377149$	$1$		$0$	$55692$	$1.216486$	$-48888643731442873/6859$	$0.97864$	$4.39012$	$[1, 1, 1, -93499, -11043164]$	\(y^2+xy+y=x^3+x^2-93499x-11043164\)	38.2.0.a.1	$[(943720/7, 913389476/7)]$
35131.b1	35131c3	35131.b	35131c	$3$	$9$	\( 19 \cdot 43^{2} \)	\( - 19 \cdot 43^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$44118$	$1296$	$43$	$1$	$1$		$0$	$243810$	$1.914040$	$-50357871050752/19$	$1.10495$	$5.17036$	$[0, -1, 1, -1422497, 653492395]$	\(y^2+y=x^3-x^2-1422497x+653492395\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$	$[ ]$
35131.b2	35131c2	35131.b	35131c	$3$	$9$	\( 19 \cdot 43^{2} \)	\( - 19^{3} \cdot 43^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$44118$	$1296$	$43$	$1$	$1$		$0$	$81270$	$1.364733$	$-89915392/6859$	$1.03310$	$3.91765$	$[0, -1, 1, -17257, 934070]$	\(y^2+y=x^3-x^2-17257x+934070\)	3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 114.24.1.?, 129.24.0.?, $\ldots$	$[ ]$
35131.b3	35131c1	35131.b	35131c	$3$	$9$	\( 19 \cdot 43^{2} \)	\( - 19 \cdot 43^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$44118$	$1296$	$43$	$1$	$1$		$0$	$27090$	$0.815427$	$32768/19$	$1.31757$	$3.14941$	$[0, -1, 1, 1233, 325]$	\(y^2+y=x^3-x^2+1233x+325\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$	$[ ]$
35131.c1	35131b1	35131.c	35131b	$1$	$1$	\( 19 \cdot 43^{2} \)	\( - 19^{2} \cdot 43^{11} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$1$	$16$	$2$	$0$	$2143680$	$2.970737$	$-510404220761669632/53070047923$	$1.01043$	$6.05162$	$[0, -1, 1, -30784617, -65738528417]$	\(y^2+y=x^3-x^2-30784617x-65738528417\)	86.2.0.?	$[ ]$
35131.d1	35131d1	35131.d	35131d	$1$	$1$	\( 19 \cdot 43^{2} \)	\( - 19^{2} \cdot 43^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$7.215444374$	$1$		$0$	$103488$	$1.363857$	$32768/15523$	$0.86481$	$3.79014$	$[0, -1, 1, 1233, -476717]$	\(y^2+y=x^3-x^2+1233x-476717\)	86.2.0.?	$[(1157/2, 39185/2)]$
35131.e1	35131a1	35131.e	35131a	$1$	$1$	\( 19 \cdot 43^{2} \)	\( - 19^{3} \cdot 43^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$19.55984801$	$1$		$0$	$2394756$	$3.097084$	$-48888643731442873/6859$	$0.97864$	$6.54619$	$[1, 0, 1, -172879690, 874896991611]$	\(y^2+xy+y=x^3-172879690x+874896991611\)	38.2.0.a.1	$[(581015791/215, 8179492880766/215)]$

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