Elliptic curves over $\Q$ of conductor 5312

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
5312.a1	5312p1	5312.a	5312p	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$996$	$12$	$1$	$0.377500059$	$1$		$4$	$3840$	$0.489812$	$-392223168/571787$	$0.96507$	$3.42321$	$[0, 0, 0, -244, 2752]$	\(y^2=x^3-244x+2752\)	3.3.0.a.1, 12.6.0.d.1, 166.2.0.?, 498.6.1.?, 996.12.1.?	$[(21, 83)]$
5312.b1	5312l1	5312.b	5312l	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{14} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$2560$	$-0.119813$	$-148176/83$	$0.66708$	$2.59826$	$[0, 0, 0, -28, -80]$	\(y^2=x^3-28x-80\)	166.2.0.?	$[]$
5312.c1	5312j1	5312.c	5312j	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.619112919$	$1$		$12$	$768$	$0.002680$	$-131096512/83$	$0.89481$	$3.14889$	$[0, -1, 0, -169, 905]$	\(y^2=x^3-x^2-169x+905\)	166.2.0.?	$[(7, 4), (8, 1)]$
5312.d1	5312f1	5312.d	5312f	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.888500034$	$1$		$10$	$512$	$-0.257542$	$8000/83$	$0.70418$	$2.34723$	$[0, -1, 0, 7, 25]$	\(y^2=x^3-x^2+7x+25\)	166.2.0.?	$[(-1, 4), (3, 8)]$
5312.e1	5312o1	5312.e	5312o	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.236223482$	$1$		$2$	$256$	$-0.341513$	$-256000/83$	$0.71692$	$2.31171$	$[0, -1, 0, -13, -19]$	\(y^2=x^3-x^2-13x-19\)	166.2.0.?	$[(5, 4)]$
5312.f1	5312h1	5312.f	5312h	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{22} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$1536$	$0.404658$	$-30664297/1328$	$0.83983$	$3.47265$	$[0, -1, 0, -417, -3263]$	\(y^2=x^3-x^2-417x-3263\)	166.2.0.?	$[]$
5312.g1	5312c1	5312.g	5312c	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.680436556$	$1$		$2$	$256$	$-0.374298$	$2048/83$	$0.76681$	$2.19063$	$[0, -1, 0, 3, 13]$	\(y^2=x^3-x^2+3x+13\)	166.2.0.?	$[(1, 4)]$
5312.h1	5312i1	5312.h	5312i	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{18} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$1024$	$0.095853$	$103823/83$	$0.77332$	$2.80110$	$[0, -1, 0, 63, 97]$	\(y^2=x^3-x^2+63x+97\)	166.2.0.?	$[]$
5312.i1	5312n1	5312.i	5312n	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$3.252201072$	$1$		$2$	$768$	$0.002680$	$-131096512/83$	$0.89481$	$3.14889$	$[0, 1, 0, -169, -905]$	\(y^2=x^3+x^2-169x-905\)	166.2.0.?	$[(18, 47)]$
5312.j1	5312a1	5312.j	5312a	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.718975858$	$1$		$2$	$256$	$-0.341513$	$-256000/83$	$0.71692$	$2.31171$	$[0, 1, 0, -13, 19]$	\(y^2=x^3+x^2-13x+19\)	166.2.0.?	$[(3, 4)]$
5312.k1	5312b1	5312.k	5312b	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.562273362$	$1$		$2$	$512$	$-0.257542$	$8000/83$	$0.70418$	$2.34723$	$[0, 1, 0, 7, -25]$	\(y^2=x^3+x^2+7x-25\)	166.2.0.?	$[(2, 1)]$
5312.l1	5312e1	5312.l	5312e	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{18} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$1024$	$0.095853$	$103823/83$	$0.77332$	$2.80110$	$[0, 1, 0, 63, -97]$	\(y^2=x^3+x^2+63x-97\)	166.2.0.?	$[]$
5312.m1	5312m1	5312.m	5312m	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.496908575$	$1$		$2$	$256$	$-0.374298$	$2048/83$	$0.76681$	$2.19063$	$[0, 1, 0, 3, -13]$	\(y^2=x^3+x^2+3x-13\)	166.2.0.?	$[(7, 20)]$
5312.n1	5312d1	5312.n	5312d	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{22} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$1536$	$0.404658$	$-30664297/1328$	$0.83983$	$3.47265$	$[0, 1, 0, -417, 3263]$	\(y^2=x^3+x^2-417x+3263\)	166.2.0.?	$[]$
5312.o1	5312k1	5312.o	5312k	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{12} \cdot 83^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$996$	$12$	$1$	$1$	$4$	$2$	$0$	$3840$	$0.489812$	$-392223168/571787$	$0.96507$	$3.42321$	$[0, 0, 0, -244, -2752]$	\(y^2=x^3-244x-2752\)	3.3.0.a.1, 12.6.0.d.1, 166.2.0.?, 498.6.1.?, 996.12.1.?	$[]$
5312.p1	5312g1	5312.p	5312g	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{14} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$2560$	$-0.119813$	$-148176/83$	$0.66708$	$2.59826$	$[0, 0, 0, -28, 80]$	\(y^2=x^3-28x+80\)	166.2.0.?	$[]$