Elliptic curve search results

Results (6 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
64.5-a2	64.5-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.5	\( 2^{6} \)	\( 2^{13} \)	$1.04210$	$(-a+2), (-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$7.156385278$	0.867839188	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -16 a - 25\) , \( -4 a - 9\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-25\right){x}-4a-9$
64.5-b2	64.5-b	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.5	\( 2^{6} \)	\( 2^{13} \)	$1.04210$	$(-a+2), (-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$7.009864600$	1.700141892	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 38 a - 95\) , \( 180 a - 461\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(38a-95\right){x}+180a-461$
128.5-a2	128.5-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.5	\( 2^{7} \)	\( 2^{7} \)	$1.23927$	$(-a+2), (-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$1$	$35.29470114$	2.140055600	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 9\) , \( -2 a + 3\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-9\right){x}-2a+3$
128.5-d2	128.5-d	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.5	\( 2^{7} \)	\( 2^{7} \)	$1.23927$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$0.327876043$	$34.57207326$	1.374613658	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -85 a - 133\) , \( -137 a - 214\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-85a-133\right){x}-137a-214$
512.2-e2	512.2-e	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.2	\( 2^{9} \)	\( 2^{25} \)	$1.75259$	$(-a+2), (-a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$12.47856126$	1.513247827	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a - 168\) , \( 192 a + 304\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a-168\right){x}+192a+304$
512.2-f2	512.2-f	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.2	\( 2^{9} \)	\( 2^{25} \)	$1.75259$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.235830817$	$12.22307372$	2.796510914	\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( 90 a - 235\) , \( -633 a + 1626\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(90a-235\right){x}-633a+1626$

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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.