Elliptic curves over \(\Q(\sqrt{-111}) \) of conductor 1.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 111

Note: The completeness Only modular elliptic curves are included

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
1.1-a1	1.1-a	$2$	$5$	\(\Q(\sqrt{-111}) \)	$2$	$[0, 1]$	1.1	\( 1 \)	\( 7^{12} \)	$0.94146$	$\textsf{none}$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Cn, 5B	$1$	\( 1 \)	$0.205572591$	$13.17843113$	1.028554772	\( 4096 \)	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -3 a - 16\) , \( 7 a - 31\bigr] \)	${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-3a-16\right){x}+7a-31$
1.1-a2	1.1-a	$2$	$5$	\(\Q(\sqrt{-111}) \)	$2$	$[0, 1]$	1.1	\( 1 \)	\( 7^{12} \)	$0.94146$	$\textsf{none}$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Cn, 5B	$1$	\( 1 \)	$1.027862956$	$2.635686227$	1.028554772	\( 38477541376 \)	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -563 a - 1486\) , \( -14287 a + 263\bigr] \)	${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-563a-1486\right){x}-14287a+263$
1.1-b1	1.1-b	$2$	$5$	\(\Q(\sqrt{-111}) \)	$2$	$[0, 1]$	1.1	\( 1 \)	\( 7^{12} \)	$0.94146$	$\textsf{none}$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Cn, 5B	$1$	\( 1 \)	$0.205572591$	$13.17843113$	1.028554772	\( 4096 \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 3 a - 19\) , \( -7 a - 24\bigr] \)	${y}^2+{y}={x}^3+a{x}^2+\left(3a-19\right){x}-7a-24$
1.1-b2	1.1-b	$2$	$5$	\(\Q(\sqrt{-111}) \)	$2$	$[0, 1]$	1.1	\( 1 \)	\( 7^{12} \)	$0.94146$	$\textsf{none}$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Cn, 5B	$1$	\( 1 \)	$1.027862956$	$2.635686227$	1.028554772	\( 38477541376 \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 563 a - 2049\) , \( 14287 a - 14024\bigr] \)	${y}^2+{y}={x}^3+a{x}^2+\left(563a-2049\right){x}+14287a-14024$

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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.