Elliptic curve search results

Results (6 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
192.1-g2	192.1-g	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	192.1	\( 2^{6} \cdot 3 \)	\( 2^{16} \cdot 3^{2} \)	$1.52431$	$(-a+2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$10.97958556$	2.395941998	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -4 a - 8\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\left(-4a-8\right){x}-4a-8$
192.1-h2	192.1-h	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	192.1	\( 2^{6} \cdot 3 \)	\( 2^{16} \cdot 3^{2} \)	$1.52431$	$(-a+2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.196629636$	$22.72318029$	1.950017184	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 15\) , \( -15 a + 42\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(6a-15\right){x}-15a+42$
576.1-e2	576.1-e	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	576.1	\( 2^{6} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{8} \)	$2.00611$	$(-a+2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.278448748$	$7.047051066$	3.425571431	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 13\) , \( 11 a - 11\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-13\right){x}+11a-11$
576.1-f2	576.1-f	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	576.1	\( 2^{6} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{8} \)	$2.00611$	$(-a+2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.128102796$	$11.80120592$	2.639157676	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -60 a - 108\) , \( -228 a - 408\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-60a-108\right){x}-228a-408$
768.1-r2	768.1-r	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	768.1	\( 2^{8} \cdot 3 \)	\( 2^{16} \cdot 3^{2} \)	$2.15570$	$(-a+2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$0.647130862$	$22.72318029$	3.208865982	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 8\) , \( 4 a + 8\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(-4a-8\right){x}+4a+8$
768.1-bh2	768.1-bh	$2$	$2$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	768.1	\( 2^{8} \cdot 3 \)	\( 2^{16} \cdot 3^{2} \)	$2.15570$	$(-a+2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$10.97958556$	1.197970999	\( -\frac{77872}{3} a + 74480 \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 15\) , \( 15 a - 42\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(6a-15\right){x}+15a-42$

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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.