Elliptic curves over \(\Q(\sqrt{373}) \)

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
3.1-a1	3.1-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	3.1	\( 3 \)	\( 3 \)	$2.27129$	$(-a-9)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.234000167$	$70.67440591$	3.425184024	\( \frac{7717}{3} a - \frac{1318768}{3} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 217085 a - 2204803\) , \( -171977812 a + 1746710581\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(217085a-2204803\right){x}-171977812a+1746710581$
3.2-a1	3.2-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	3.2	\( 3 \)	\( 3 \)	$2.27129$	$(-a+10)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.234000167$	$70.67440591$	3.425184024	\( -\frac{7717}{3} a - 437017 \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -217083 a - 1987720\) , \( 172194896 a + 1576720488\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-217083a-1987720\right){x}+172194896a+1576720488$
7.1-a1	7.1-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	7.1	\( 7 \)	\( 7^{2} \)	$2.80716$	$(6a+55)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cn	$1$	\( 2 \)	$1$	$33.65332822$	3.485006569	\( \frac{282320896}{49} a + \frac{2585579520}{49} \)	\( \bigl[0\) , \( a\) , \( 1\) , \( -12 a - 82\) , \( 35 a + 292\bigr] \)	${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-12a-82\right){x}+35a+292$
7.2-a1	7.2-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	7.2	\( 7 \)	\( 7^{2} \)	$2.80716$	$(-6a+61)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cn	$1$	\( 2 \)	$1$	$33.65332822$	3.485006569	\( -\frac{282320896}{49} a + \frac{2867900416}{49} \)	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 12 a - 94\) , \( -35 a + 327\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a-94\right){x}-35a+327$
9.2-a1	9.2-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	9.2	\( 3^{2} \)	\( 3^{7} \)	$2.98919$	$(-a-9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$0.874044854$	$9.824887300$	3.557106504	\( \frac{7717}{3} a - \frac{1318768}{3} \)	\( \bigl[a\) , \( -a\) , \( a\) , \( 5312 a - 53922\) , \( 711717 a - 7228512\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(5312a-53922\right){x}+711717a-7228512$
9.3-a1	9.3-a	$1$	$1$	\(\Q(\sqrt{373}) \)	$2$	$[2, 0]$	9.3	\( 3^{2} \)	\( 3^{7} \)	$2.98919$	$(-a+10)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$0.874044854$	$9.824887300$	3.557106504	\( -\frac{7717}{3} a - 437017 \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5314 a - 48610\) , \( -711718 a - 6516795\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5314a-48610\right){x}-711718a-6516795$

 

  *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.