Elliptic curve search results

Results (5 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
320.1-a2	320.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	320.1	\( 2^{6} \cdot 5 \)	\( - 2^{16} \cdot 5 \)	$0.84511$	$(-2a+1), (2)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$17.62784313$	0.985426388	\( -\frac{237035808}{5} a + \frac{383532624}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 \phi + 1\) , \( 36 \phi + 26\bigr] \)	${y}^2={x}^{3}+\left(9\phi+1\right){x}+36\phi+26$
1280.1-a2	1280.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( - 2^{16} \cdot 5 \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 1 \)	$1$	$11.98755592$	1.340249496	\( -\frac{237035808}{5} a + \frac{383532624}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 \phi - 7\) , \( -16 \phi + 6\bigr] \)	${y}^2={x}^{3}+\left(8\phi-7\right){x}-16\phi+6$
1280.1-i2	1280.1-i	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( - 2^{16} \cdot 5 \)	$1.19516$	$(-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 1 \)	$1.866787005$	$4.075980709$	1.701421401	\( -\frac{237035808}{5} a + \frac{383532624}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 \phi + 1\) , \( -36 \phi - 26\bigr] \)	${y}^2={x}^{3}+\left(9\phi+1\right){x}-36\phi-26$
1280.1-j2	1280.1-j	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1280.1	\( 2^{8} \cdot 5 \)	\( - 2^{16} \cdot 5 \)	$1.19516$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$1$	$5.993777963$	1.340249496	\( -\frac{237035808}{5} a + \frac{383532624}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 \phi - 7\) , \( 16 \phi - 6\bigr] \)	${y}^2={x}^{3}+\left(8\phi-7\right){x}+16\phi-6$
1600.1-a2	1600.1-a	$8$	$16$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	1600.1	\( 2^{6} \cdot 5^{2} \)	\( - 2^{16} \cdot 5^{7} \)	$1.26373$	$(-2a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$1.822833988$	1.630392283	\( -\frac{237035808}{5} a + \frac{383532624}{5} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 40 \phi - 35\) , \( -20 \phi - 190\bigr] \)	${y}^2={x}^{3}+\left(40\phi-35\right){x}-20\phi-190$

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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.