Elliptic curves over \(\Q(\sqrt{118}) \)

Results (6 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1.1-a1	1.1-a	$2$	$2$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.94138$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓		✓	✓	$59$	59Ns.3.1	$1$	\( 1 \)	$1$	$50.75994773$	0.584103993	\( 8000 \)	\( \bigl[a\) , \( 0\) , \( 1\) , \( -11773 a - 127592\) , \( -2144822 a - 23297780\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-11773a-127592\right){x}-2144822a-23297780$
1.1-a2	1.1-a	$2$	$2$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.94138$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-8$	$N(\mathrm{U}(1))$	✓		✓	✓	$59$	59Ns.3.1	$1$	\( 1 \)	$1$	$50.75994773$	0.584103993	\( 8000 \)	\( \bigl[a\) , \( 0\) , \( 1\) , \( 11772 a - 127592\) , \( 2144822 a - 23297780\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(11772a-127592\right){x}+2144822a-23297780$
6.1-a1	6.1-a	$1$	$1$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	6.1	\( 2 \cdot 3 \)	\( 2^{4} \cdot 3^{4} \)	$3.03842$	$(51a+554), (a+11)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{4} \)	$1$	$5.987857893$	4.409815993	\( -\frac{719883875}{81} a - \frac{31282006553}{324} \)	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 107140 a - 1163808\) , \( -69894747 a + 759251261\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(107140a-1163808\right){x}-69894747a+759251261$
6.1-b1	6.1-b	$1$	$1$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	6.1	\( 2 \cdot 3 \)	\( 2^{4} \cdot 3^{4} \)	$3.03842$	$(51a+554), (a+11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{3} \)	$0.409811308$	$12.77578609$	3.855853759	\( -\frac{719883875}{81} a - \frac{31282006553}{324} \)	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -388472 a - 4219684\) , \( 429845391 a + 4669316660\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-388472a-4219684\right){x}+429845391a+4669316660$
6.2-a1	6.2-a	$1$	$1$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	6.2	\( 2 \cdot 3 \)	\( 2^{4} \cdot 3^{4} \)	$3.03842$	$(51a+554), (-a+11)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{4} \)	$1$	$5.987857893$	4.409815993	\( \frac{719883875}{81} a - \frac{31282006553}{324} \)	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -107140 a - 1163808\) , \( 69894747 a + 759251261\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-107140a-1163808\right){x}+69894747a+759251261$
6.2-b1	6.2-b	$1$	$1$	\(\Q(\sqrt{118}) \)	$2$	$[2, 0]$	6.2	\( 2 \cdot 3 \)	\( 2^{4} \cdot 3^{4} \)	$3.03842$	$(51a+554), (-a+11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{3} \)	$0.409811308$	$12.77578609$	3.855853759	\( \frac{719883875}{81} a - \frac{31282006553}{324} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 388471 a - 4219684\) , \( -429845391 a + 4669316660\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(388471a-4219684\right){x}-429845391a+4669316660$

 

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.