Elliptic curves over \(\Q(\sqrt{-106}) \) of conductor 55.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100 over imaginary quadratic fields with absolute discriminant 424

Note: The completeness Only modular elliptic curves are included

Results (displaying both 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
55.2-a1	55.2-a	$1$	$1$	\(\Q(\sqrt{-106}) \)	$2$	$[0, 1]$	55.2	\( 5 \cdot 11 \)	\( 5^{10} \cdot 11^{14} \)	$5.01086$	$(5,a+2), (11,a+9)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{2} \)	$1$	$1.084708409$	0.421424777	\( -\frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \)	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -161 a - 24501\) , \( 16064 a + 1727907\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-161a-24501\right){x}+16064a+1727907$
55.2-b1	55.2-b	$1$	$1$	\(\Q(\sqrt{-106}) \)	$2$	$[0, 1]$	55.2	\( 5 \cdot 11 \)	\( 5^{22} \cdot 11^{2} \)	$5.01086$	$(5,a+2), (11,a+9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2^{2} \cdot 5 \)	$1.346990674$	$1.084708409$	5.676552447	\( -\frac{2734676695743488}{1181640625} a + \frac{17162649294593856}{1181640625} \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -353 a - 3217\) , \( 17287 a + 60545\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-353a-3217\right){x}+17287a+60545$

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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.