Elliptic curve search results

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
1024.1-b1	1024.1-b	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( - 2^{24} \)	$1.13031$	$(2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$13.36728142$	1.494507497	\( -7232 a + 12032 \)	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 5 \phi - 6\) , \( -2 \phi + 5\bigr] \)	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(5\phi-6\right){x}-2\phi+5$
1024.1-d1	1024.1-d	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( - 2^{24} \)	$1.13031$	$(2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$9.711302806$	1.085756661	\( -7232 a + 12032 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 \phi - 1\) , \( -4 \phi - 1\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\left(4\phi-1\right){x}-4\phi-1$
1024.1-g1	1024.1-g	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( - 2^{24} \)	$1.13031$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2 \)	$1$	$6.313756918$	1.411798966	\( -7232 a + 12032 \)	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 5 \phi - 6\) , \( 2 \phi - 5\bigr] \)	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(5\phi-6\right){x}+2\phi-5$
1024.1-i1	1024.1-i	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1024.1	\( 2^{10} \)	\( - 2^{24} \)	$1.13031$	$(2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.189728863$	$8.690673875$	1.474795663	\( -7232 a + 12032 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 \phi - 1\) , \( 4 \phi + 1\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(4\phi-1\right){x}+4\phi+1$
4096.1-h1	4096.1-h	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	4096.1	\( 2^{12} \)	\( - 2^{12} \)	$1.59850$	$(2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 1 \)	$0.609025663$	$19.42260561$	2.645014686	\( -7232 a + 12032 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( \phi\) , \( -\phi\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\phi{x}-\phi$
4096.1-o1	4096.1-o	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	4096.1	\( 2^{12} \)	\( - 2^{12} \)	$1.59850$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 1 \)	$1$	$17.38134775$	1.943293755	\( -7232 a + 12032 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( \phi\) , \( \phi\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\phi{x}+\phi$
4096.1-t1	4096.1-t	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	4096.1	\( 2^{12} \)	\( - 2^{12} \)	$1.59850$	$(2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 1 \)	$0.382578113$	$26.73456285$	2.287063434	\( -7232 a + 12032 \)	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( \phi - 1\) , \( -\phi + 2\bigr] \)	${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-1\right){x}-\phi+2$
4096.1-z1	4096.1-z	$4$	$4$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	4096.1	\( 2^{12} \)	\( - 2^{12} \)	$1.59850$	$(2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 1 \)	$1$	$12.62751383$	1.411798966	\( -7232 a + 12032 \)	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( \phi - 1\) , \( \phi - 2\bigr] \)	${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(\phi-1\right){x}+\phi-2$

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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.