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
33.1-a4	33.1-a	$4$	$4$	\(\Q(\sqrt{165}) \)	$2$	$[2, 0]$	33.1	\( 3 \cdot 11 \)	\( 3^{6} \cdot 11^{8} \)	$2.75112$	$(3,a+1), (a+5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{4} \)	$2.146444646$	$8.936252827$	2.986504436	\( \frac{347873904937}{395307} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$
33.1-b4	33.1-b	$4$	$4$	\(\Q(\sqrt{165}) \)	$2$	$[2, 0]$	33.1	\( 3 \cdot 11 \)	\( 3^{18} \cdot 11^{8} \)	$2.75112$	$(3,a+1), (a+5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$6.147048426$	$1.883253066$	5.407351434	\( \frac{347873904937}{395307} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1319\) , \( -18084\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1319{x}-18084$
33.1-c4	33.1-c	$4$	$4$	\(\Q(\sqrt{165}) \)	$2$	$[2, 0]$	33.1	\( 3 \cdot 11 \)	\( 3^{6} \cdot 11^{8} \)	$2.75112$	$(3,a+1), (a+5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$1.883253066$	0.586444209	\( \frac{347873904937}{395307} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1913 a - 13137\) , \( 115761 a - 801162\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1913a-13137\right){x}+115761a-801162$
33.1-d4	33.1-d	$4$	$4$	\(\Q(\sqrt{165}) \)	$2$	$[2, 0]$	33.1	\( 3 \cdot 11 \)	\( 3^{18} \cdot 11^{8} \)	$2.75112$	$(3,a+1), (a+5)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{4} \cdot 3 \)	$0.157947687$	$8.936252827$	5.274338318	\( \frac{347873904937}{395307} \)	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 17137 a - 118632\) , \( -3003792 a + 20794100\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17137a-118632\right){x}-3003792a+20794100$

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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.