Elliptic curves over \(\Q(\sqrt{-17}) \) of conductor 169.2

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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
169.2-a1	169.2-a	$2$	$2$	\(\Q(\sqrt{-17}) \)	$2$	$[0, 1]$	169.2	\( 13^{2} \)	\( 2^{12} \cdot 13^{4} \)	$2.65684$	$(13,a+3), (13,a+10)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	\( 2^{2} \)	$1.119007573$	$4.740653744$	2.573219280	\( \frac{9129329}{169} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 19\) , \( 10 a - 17\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-a+19\right){x}+10a-17$
169.2-a2	169.2-a	$2$	$2$	\(\Q(\sqrt{-17}) \)	$2$	$[0, 1]$	169.2	\( 13^{2} \)	\( 2^{12} \cdot 13^{2} \)	$2.65684$	$(13,a+3), (13,a+10)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$4$	\( 1 \)	$2.238015147$	$2.370326872$	2.573219280	\( \frac{36892780289}{13} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 279\) , \( 478 a - 277\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-a+279\right){x}+478a-277$
169.2-b1	169.2-b	$2$	$2$	\(\Q(\sqrt{-17}) \)	$2$	$[0, 1]$	169.2	\( 13^{2} \)	\( 2^{12} \cdot 13^{4} \)	$2.65684$	$(13,a+3), (13,a+10)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	\( 2^{2} \)	$1.119007573$	$4.740653744$	2.573219280	\( \frac{9129329}{169} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( a + 19\) , \( -10 a - 17\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a+19\right){x}-10a-17$
169.2-b2	169.2-b	$2$	$2$	\(\Q(\sqrt{-17}) \)	$2$	$[0, 1]$	169.2	\( 13^{2} \)	\( 2^{12} \cdot 13^{2} \)	$2.65684$	$(13,a+3), (13,a+10)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$4$	\( 1 \)	$2.238015147$	$2.370326872$	2.573219280	\( \frac{36892780289}{13} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( a + 279\) , \( -478 a - 277\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a+279\right){x}-478a-277$

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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.