Elliptic curves over \(\Q(\sqrt{-57}) \) of conductor 81.1

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 228

Note: The completeness Only modular elliptic curves are included

Results (8 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
81.1-a1	81.1-a	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{10} \)	$4.04788$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs	$1$	\( 3 \)	$1$	$2.702876088$	1.074014050	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( -49\bigr] \)	${y}^2+a{y}={x}^3-30{x}-49$
81.1-a2	81.1-a	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{22} \)	$4.04788$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs	$1$	\( 3 \)	$1$	$2.702876088$	1.074014050	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( -270\) , \( 1722\bigr] \)	${y}^2+a{y}={x}^3-270{x}+1722$
81.1-a3	81.1-a	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{6} \)	$4.04788$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs	$1$	\( 1 \)	$1$	$8.108628264$	1.074014050	\( 0 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 14\bigr] \)	${y}^2+a{y}={x}^3+14$
81.1-a4	81.1-a	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{18} \)	$4.04788$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs	$1$	\( 1 \)	$1$	$8.108628264$	1.074014050	\( 0 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 21\bigr] \)	${y}^2+a{y}={x}^3+21$
81.1-b1	81.1-b	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{10} \)	$4.04788$	$(3,a)$	0	$\Z/3\Z$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$9$	\( 1 \)	$1$	$2.702876088$	0.358004683	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \)	${y}^2+{y}={x}^3-30{x}+63$
81.1-b2	81.1-b	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{22} \)	$4.04788$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 1 \)	$1$	$2.702876088$	0.358004683	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \)	${y}^2+{y}={x}^3-270{x}-1708$
81.1-b3	81.1-b	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{18} \)	$4.04788$	$(3,a)$	0	$\Z/3\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 3 \)	$1$	$8.108628264$	0.358004683	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -7\bigr] \)	${y}^2+{y}={x}^3-7$
81.1-b4	81.1-b	$4$	$27$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{6} \)	$4.04788$	$(3,a)$	0	$\Z/3\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 3 \)	$1$	$8.108628264$	0.358004683	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{y}={x}^3$

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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.