Elliptic curves over \(\Q(\sqrt{-219}) \) 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 219

Note: The completeness Only modular elliptic curves are included

Results (6 matches)

  Download displayed columns for results to

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	$4$	$27$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{10} \)	$3.96718$	$(3,a+1)$	0	$\Z/3\Z$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$9$	\( 1 \)	$1$	$2.702876088$	0.365286880	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \)	${y}^2+{y}={x}^3-30{x}+63$
81.1-a2	81.1-a	$4$	$27$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{22} \)	$3.96718$	$(3,a+1)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-27$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 1 \)	$1$	$2.702876088$	0.365286880	\( -12288000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \)	${y}^2+{y}={x}^3-270{x}-1708$
81.1-a3	81.1-a	$4$	$27$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{18} \)	$3.96718$	$(3,a+1)$	0	$\Z/3\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 3 \)	$1$	$8.108628264$	0.365286880	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -7\bigr] \)	${y}^2+{y}={x}^3-7$
81.1-a4	81.1-a	$4$	$27$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{6} \)	$3.96718$	$(3,a+1)$	0	$\Z/3\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$3$	3Cs.1.1	$1$	\( 3 \)	$1$	$8.108628264$	0.365286880	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{y}={x}^3$
81.1-b1	81.1-b	$1$	$1$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{10} \cdot 5^{12} \)	$3.96718$	$(3,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cn	$4$	\( 1 \)	$1$	$4.914669842$	2.656820892	\( -12288 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -9 a - 30\) , \( -36 a + 36\bigr] \)	${y}^2+{y}={x}^3+\left(-9a-30\right){x}-36a+36$
81.1-c1	81.1-c	$1$	$1$	\(\Q(\sqrt{-219}) \)	$2$	$[0, 1]$	81.1	\( 3^{4} \)	\( 3^{10} \cdot 5^{12} \)	$3.96718$	$(3,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cn	$4$	\( 1 \)	$1$	$4.914669842$	2.656820892	\( -12288 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 9 a - 39\) , \( 36 a\bigr] \)	${y}^2+{y}={x}^3+\left(9a-39\right){x}+36a$

  Download displayed columns for results to

  *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.