Elliptic curves over \(\Q(\sqrt{-1247}) \)

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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
9.1-a1	9.1-a	$2$	$43$	\(\Q(\sqrt{-1247}) \)	$2$	$[0, 1]$	9.1	\( 3^{2} \)	\( 3^{6} \cdot 13^{12} \)	$5.46553$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-43$	$N(\mathrm{U}(1))$	✓			✓	$29, 43$	29Nn.1.2.1, 43B.42.13	$1$	\( 2 \)	$1$	$4.823892952$	0.273208640	\( -884736000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -320 a + 8580\) , \( -14070 a - 297502\bigr] \)	${y}^2+{y}={x}^3+\left(-320a+8580\right){x}-14070a-297502$
9.1-a2	9.1-a	$2$	$43$	\(\Q(\sqrt{-1247}) \)	$2$	$[0, 1]$	9.1	\( 3^{2} \)	\( 3^{6} \cdot 73^{12} \)	$5.46553$	$(3,a)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-43$	$N(\mathrm{U}(1))$	✓			✓	$29, 43$	29Nn.1.2.1, 43B.42.13	$1$	\( 2 \)	$1$	$4.823892952$	0.273208640	\( -884736000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -6080 a - 298140\) , \( -1936410 a - 59643187\bigr] \)	${y}^2+{y}={x}^3+\left(-6080a-298140\right){x}-1936410a-59643187$
9.3-a1	9.3-a	$2$	$43$	\(\Q(\sqrt{-1247}) \)	$2$	$[0, 1]$	9.3	\( 3^{2} \)	\( 3^{6} \cdot 73^{12} \)	$5.46553$	$(3,a+2)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-43$	$N(\mathrm{U}(1))$	✓			✓	$29, 43$	29Nn.1.2.1, 43B.42.13	$1$	\( 2 \)	$1$	$4.823892952$	0.273208640	\( -884736000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6080 a - 304220\) , \( 1936410 a - 61579597\bigr] \)	${y}^2+{y}={x}^3+\left(6080a-304220\right){x}+1936410a-61579597$
9.3-a2	9.3-a	$2$	$43$	\(\Q(\sqrt{-1247}) \)	$2$	$[0, 1]$	9.3	\( 3^{2} \)	\( 3^{6} \cdot 13^{12} \)	$5.46553$	$(3,a+2)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-43$	$N(\mathrm{U}(1))$	✓			✓	$29, 43$	29Nn.1.2.1, 43B.42.13	$1$	\( 2 \)	$1$	$4.823892952$	0.273208640	\( -884736000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 320 a + 8260\) , \( 14070 a - 311572\bigr] \)	${y}^2+{y}={x}^3+\left(320a+8260\right){x}+14070a-311572$

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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.