Elliptic curve search results

Results (4 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
1458.4-c2	1458.4-c	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.4	\( 2 \cdot 3^{6} \)	\( 2^{9} \cdot 3^{20} \)	$1.56179$	$(a), (-a-1), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 1 \)	$1$	$1.229597065$	0.869456422	\( \frac{90933}{32} a + \frac{32829}{8} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a - 15\) , \( -54 a + 35\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a-15\right){x}-54a+35$
1458.4-d2	1458.4-d	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	1458.4	\( 2 \cdot 3^{6} \)	\( 2^{9} \cdot 3^{8} \)	$1.56179$	$(a), (-a-1), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 3^{2} \)	$1$	$3.688791195$	2.608369268	\( \frac{90933}{32} a + \frac{32829}{8} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 2\) , \( 3 a - 1\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a-2\right){x}+3a-1$
11664.4-h2	11664.4-h	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	11664.4	\( 2^{4} \cdot 3^{6} \)	\( 2^{21} \cdot 3^{8} \)	$2.62661$	$(a), (-a-1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{2} \cdot 3 \)	$0.123865268$	$1.844395597$	3.877036303	\( \frac{90933}{32} a + \frac{32829}{8} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -12 a - 6\) , \( 24 a - 6\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-12a-6\right){x}+24a-6$
11664.4-k2	11664.4-k	$3$	$9$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	11664.4	\( 2^{4} \cdot 3^{6} \)	\( 2^{21} \cdot 3^{20} \)	$2.62661$	$(a), (-a-1), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2 \cdot 3 \)	$1$	$0.614798532$	2.608369268	\( \frac{90933}{32} a + \frac{32829}{8} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -108 a - 60\) , \( -432 a + 280\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-108a-60\right){x}-432a+280$

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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.