Elliptic curves over \(\Q(\sqrt{173}) \)

Results (4 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
4.1-a1	4.1-a	$1$	$1$	\(\Q(\sqrt{173}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$1.66217$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 3 \)	$0.321558588$	$18.56376528$	2.723042259	\( \frac{8266131}{8} a + \frac{12564855}{2} \)	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( a + 9\) , \( -23 a - 134\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(a+9\right){x}-23a-134$
4.1-b1	4.1-b	$2$	$5$	\(\Q(\sqrt{173}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{2} \)	$1.66217$	$(2)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$5$	5B.1.1	$9$	\( 1 \)	$1$	$65.53394125$	1.793683184	\( \frac{24389}{2} \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 16 a - 23\) , \( -5 a + 261\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a-23\right){x}-5a+261$
4.1-b2	4.1-b	$2$	$5$	\(\Q(\sqrt{173}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{10} \)	$1.66217$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$5$	5B.1.2	$9$	\( 1 \)	$1$	$2.621357650$	1.793683184	\( \frac{47792627189}{32} \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 991 a - 6923\) , \( 43738 a - 309288\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(991a-6923\right){x}+43738a-309288$
4.1-c1	4.1-c	$1$	$1$	\(\Q(\sqrt{173}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$1.66217$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 3 \)	$0.321558588$	$18.56376528$	2.723042259	\( -\frac{8266131}{8} a + \frac{58525551}{8} \)	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -a + 10\) , \( 24 a - 167\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+10\right){x}+24a-167$

 

  *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.