Elliptic curves over \(\Q(\sqrt{-11}) \) of conductor 1089.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 50000 over imaginary quadratic fields with absolute discriminant 11

Note: The completeness Only modular elliptic curves are included

Results (7 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
1089.1-a1	1089.1-a	$2$	$11$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{10} \)	$1.70252$	$(-a), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$11$	11B.10.4[2]	$1$	\( 2 \)	$1.143742936$	$0.490498967$	1.353194323	\( -24729001 \)	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 328 a - 992\) , \( 5020 a - 10528\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(328a-992\right){x}+5020a-10528$
1089.1-a2	1089.1-a	$2$	$11$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{2} \)	$1.70252$	$(-a), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$11$	11B.10.2[2]	$1$	\( 2 \)	$0.103976630$	$5.395488645$	1.353194323	\( -121 \)	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 2\) , \( -2 a + 2\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}-2a+2$
1089.1-b1	1089.1-b	$2$	$2$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{3} \cdot 11^{8} \)	$1.70252$	$(-a), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$1.280829557$	1.544738568	\( -\frac{393194}{11} a - 1506561 \)	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -60 a + 3\) , \( -213 a + 267\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-60a+3\right){x}-213a+267$
1089.1-b2	1089.1-b	$2$	$2$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{3} \cdot 11^{7} \)	$1.70252$	$(-a), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$2.561659115$	1.544738568	\( -\frac{7136}{11} a + \frac{11895}{11} \)	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -5 a + 3\) , \( -4 a + 3\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a+3\right){x}-4a+3$
1089.1-c1	1089.1-c	$3$	$25$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{8} \)	$1.70252$	$(-a), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2Cn, 5B.4.2	$1$	\( 2^{2} \)	$9.765222448$	$0.064462474$	3.036775978	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 86024 a - 258072\) , \( 23367062 a - 44006795\bigr] \)	${y}^2+{y}={x}^{3}+a{x}^{2}+\left(86024a-258072\right){x}+23367062a-44006795$
1089.1-c2	1089.1-c	$3$	$25$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{16} \)	$1.70252$	$(-a), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2Cn, 5Cs.4.1	$1$	\( 2^{2} \)	$1.953044489$	$0.322312373$	3.036775978	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 114 a - 342\) , \( 1962 a - 3935\bigr] \)	${y}^2+{y}={x}^{3}+a{x}^{2}+\left(114a-342\right){x}+1962a-3935$
1089.1-c3	1089.1-c	$3$	$25$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{8} \)	$1.70252$	$(-a), (-2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 5$	2Cn, 5B.4.1	$1$	\( 2^{2} \)	$0.390608897$	$1.611561869$	3.036775978	\( -\frac{4096}{11} \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 4 a - 12\) , \( -18 a + 25\bigr] \)	${y}^2+{y}={x}^{3}+a{x}^{2}+\left(4a-12\right){x}-18a+25$

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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.