Elliptic curves over \(\Q(\sqrt{26}) \) of conductor 16.1

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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
16.1-a1	16.1-a	$1$	$1$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{20} \)	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.326166095$	$24.54409375$	3.139996309	\( -23504 a - 119652 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 22\) , \( 10 a - 58\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+22\right){x}+10a-58$
16.1-b1	16.1-b	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{24} \)	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.2	$1$	\( 1 \)	$1$	$21.28911211$	2.087569194	\( -23788477376 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9586 a - 48883\) , \( -1173397 a + 5983175\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9586a-48883\right){x}-1173397a+5983175$
16.1-b2	16.1-b	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{24} \)	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.1	$1$	\( 1 \)	$1$	$21.28911211$	2.087569194	\( 64 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a + 77\) , \( -277 a + 1415\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a+77\right){x}-277a+1415$
16.1-c1	16.1-c	$1$	$1$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{20} \)	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.326166095$	$24.54409375$	3.139996309	\( 23504 a - 119652 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 22\) , \( -10 a - 58\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+22\right){x}-10a-58$
16.1-d1	16.1-d	$1$	$1$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{8} \)	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.269173633$	$24.54409375$	2.591330699	\( 23504 a - 119652 \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -3 a + 22\) , \( -6 a + 13\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+22\right){x}-6a+13$
16.1-e1	16.1-e	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{12} \)	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.2	$1$	\( 1 \)	$1$	$21.28911211$	2.087569194	\( -23788477376 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2396 a - 12214\) , \( -139366 a + 710632\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2396a-12214\right){x}-139366a+710632$
16.1-e2	16.1-e	$2$	$5$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{12} \)	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.1	$1$	\( 1 \)	$1$	$21.28911211$	2.087569194	\( 64 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 26\) , \( -46 a + 232\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+26\right){x}-46a+232$
16.1-f1	16.1-f	$1$	$1$	\(\Q(\sqrt{26}) \)	$2$	$[2, 0]$	16.1	\( 2^{4} \)	\( 2^{8} \)	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.269173633$	$24.54409375$	2.591330699	\( -23504 a - 119652 \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3 a + 22\) , \( 6 a + 13\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+22\right){x}+6a+13$

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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.