Elliptic curves over \(\Q(\sqrt{-14}) \) of conductor 288.2

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 56

Note: The completeness Only modular elliptic curves are included

Results (16 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
288.2-a1	288.2-a	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{8} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.337900933$	$4.690728597$	1.694437954	\( \frac{97336}{81} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 11\) , \( 2\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+11{x}+2$
288.2-a2	288.2-a	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{4} \cdot 7^{12} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$0.675801867$	$4.690728597$	1.694437954	\( \frac{21952}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -114\) , \( -216\bigr] \)	${y}^2={x}^3-{x}^2-114{x}-216$
288.2-a3	288.2-a	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$1.351603734$	$4.690728597$	1.694437954	\( \frac{140608}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \)	${y}^2={x}^3-{x}^2-4{x}-2$
288.2-a4	288.2-a	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1.351603734$	$4.690728597$	1.694437954	\( \frac{7301384}{3} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -6\) , \( 15\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2-6{x}+15$
288.2-b1	288.2-b	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{8} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1$	$4.690728597$	2.507299900	\( \frac{97336}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \)	${y}^2={x}^3-{x}^2+8{x}-8$
288.2-b2	288.2-b	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{4} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{3} \)	$1$	$4.690728597$	2.507299900	\( \frac{21952}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)	${y}^2={x}^3-{x}^2-2{x}$
288.2-b3	288.2-b	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{24} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$16$	\( 2 \)	$1$	$4.690728597$	2.507299900	\( \frac{140608}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \)	${y}^2={x}^3-{x}^2-17{x}+33$
288.2-b4	288.2-b	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1$	$4.690728597$	2.507299900	\( \frac{7301384}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \)	${y}^2={x}^3-{x}^2-32{x}-60$
288.2-c1	288.2-c	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{8} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{5} \)	$1$	$4.690728597$	2.507299900	\( \frac{97336}{81} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( 13\) , \( -1\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+13{x}-1$
288.2-c2	288.2-c	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{4} \cdot 7^{12} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{3} \)	$1$	$4.690728597$	2.507299900	\( \frac{21952}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -114\) , \( 216\bigr] \)	${y}^2={x}^3+{x}^2-114{x}+216$
288.2-c3	288.2-c	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1$	$4.690728597$	2.507299900	\( \frac{140608}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 2\bigr] \)	${y}^2={x}^3+{x}^2-4{x}+2$
288.2-c4	288.2-c	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{6} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1$	$4.690728597$	2.507299900	\( \frac{7301384}{3} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)	${y}^2+a{x}{y}={x}^3-4{x}-1$
288.2-d1	288.2-d	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{8} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{5} \)	$1.353236516$	$4.690728597$	6.785939565	\( \frac{97336}{81} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( 8\bigr] \)	${y}^2={x}^3+{x}^2+8{x}+8$
288.2-d2	288.2-d	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{12} \cdot 3^{4} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$2.706473032$	$4.690728597$	6.785939565	\( \frac{21952}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)	${y}^2={x}^3+{x}^2-2{x}$
288.2-d3	288.2-d	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{24} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$5.412946065$	$4.690728597$	6.785939565	\( \frac{140608}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( -33\bigr] \)	${y}^2={x}^3+{x}^2-17{x}-33$
288.2-d4	288.2-d	$4$	$4$	\(\Q(\sqrt{-14}) \)	$2$	$[0, 1]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{18} \cdot 3^{2} \)	$2.75474$	$(2,a), (3,a+1), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1.353236516$	$4.690728597$	6.785939565	\( \frac{7301384}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -32\) , \( 60\bigr] \)	${y}^2={x}^3+{x}^2-32{x}+60$

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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.