Elliptic curve search results

Results (12 matches)

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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
3456.2-a2	3456.2-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	3456.2	\( 2^{7} \cdot 3^{3} \)	\( 2^{8} \cdot 3^{10} \)	$1.93788$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.535885794$	$3.397541734$	2.574850644	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 3\) , \( 2 a - 2\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-3\right){x}+2a-2$
3456.2-h2	3456.2-h	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	3456.2	\( 2^{7} \cdot 3^{3} \)	\( 2^{8} \cdot 3^{10} \)	$1.93788$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$3.397541734$	2.402424800	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 3\) , \( -2 a + 2\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-3\right){x}-2a+2$
6912.2-g2	6912.2-g	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	6912.2	\( 2^{8} \cdot 3^{3} \)	\( 2^{8} \cdot 3^{4} \)	$2.30454$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$5.884714905$	2.080560907	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( a\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}+a$
6912.2-h2	6912.2-h	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	6912.2	\( 2^{8} \cdot 3^{3} \)	\( 2^{8} \cdot 3^{4} \)	$2.30454$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$5.884714905$	2.080560907	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -a\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-a$
10368.3-a2	10368.3-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	10368.3	\( 2^{7} \cdot 3^{4} \)	\( 2^{8} \cdot 3^{10} \)	$2.55039$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.392504916$	$3.397541734$	3.771854182	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a\) , \( 2 a - 1\bigr] \)	${y}^2={x}^{3}-3a{x}+2a-1$
10368.3-p2	10368.3-p	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	10368.3	\( 2^{7} \cdot 3^{4} \)	\( 2^{8} \cdot 3^{10} \)	$2.55039$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.222854408$	$3.397541734$	4.283127666	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a\) , \( -2 a + 1\bigr] \)	${y}^2={x}^{3}-3a{x}-2a+1$
20736.3-a2	20736.3-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	20736.3	\( 2^{8} \cdot 3^{4} \)	\( 2^{8} \cdot 3^{16} \)	$3.03295$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.744955985$	$1.961571635$	4.133136802	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 12\) , \( -11 a + 1\bigr] \)	${y}^2={x}^{3}+\left(3a+12\right){x}-11a+1$
20736.3-z2	20736.3-z	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	20736.3	\( 2^{8} \cdot 3^{4} \)	\( 2^{8} \cdot 3^{16} \)	$3.03295$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$1.961571635$	1.387040605	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 12\) , \( 11 a - 1\bigr] \)	${y}^2={x}^{3}+\left(3a+12\right){x}+11a-1$
27648.2-a2	27648.2-a	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	27648.2	\( 2^{10} \cdot 3^{3} \)	\( 2^{14} \cdot 3^{4} \)	$3.25911$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.500028323$	$4.161121815$	2.942524130	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3\) , \( -a + 1\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}-3{x}-a+1$
27648.2-x2	27648.2-x	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	27648.2	\( 2^{10} \cdot 3^{3} \)	\( 2^{14} \cdot 3^{10} \)	$3.25911$	$(a), (-a-1), (a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1.306559505$	$2.402424800$	4.439090448	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a + 5\) , \( -a + 13\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a+5\right){x}-a+13$
27648.2-y2	27648.2-y	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	27648.2	\( 2^{10} \cdot 3^{3} \)	\( 2^{14} \cdot 3^{10} \)	$3.25911$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$2.402424800$	1.698770867	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 5\) , \( a - 13\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+5\right){x}+a-13$
27648.2-bv2	27648.2-bv	$2$	$2$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	27648.2	\( 2^{10} \cdot 3^{3} \)	\( 2^{14} \cdot 3^{4} \)	$3.25911$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$4.161121815$	2.942357452	\( -\frac{3584}{3} a + \frac{4096}{3} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3\) , \( a - 1\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-3{x}+a-1$

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  *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.