Elliptic curve search results

Results (4 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
96.6-a3	96.6-a	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.6	\( 2^{5} \cdot 3 \)	\( 2^{9} \cdot 3 \)	$2.11176$	$(a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$1$	$36.45010896$	1.206983718	\( -\frac{153722875}{3} a + \frac{657508625}{3} \)	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -157 a - 513\) , \( 1572 a + 5148\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-157a-513\right){x}+1572a+5148$
96.6-b3	96.6-b	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.6	\( 2^{5} \cdot 3 \)	\( 2^{9} \cdot 3 \)	$2.11176$	$(a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$16$	\( 1 \)	$1$	$6.231612613$	3.301589017	\( -\frac{153722875}{3} a + \frac{657508625}{3} \)	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1771 a - 7536\) , \( 76789 a - 328227\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1771a-7536\right){x}+76789a-328227$
192.6-g3	192.6-g	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.6	\( 2^{6} \cdot 3 \)	\( 2^{15} \cdot 3 \)	$2.51132$	$(a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$13.86747782$	1.836792309	\( -\frac{153722875}{3} a + \frac{657508625}{3} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 135 a - 566\) , \( -1618 a + 6923\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(135a-566\right){x}-1618a+6923$
192.6-j3	192.6-j	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.6	\( 2^{6} \cdot 3 \)	\( 2^{15} \cdot 3 \)	$2.51132$	$(a+3), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$3.128105331$	$8.189771841$	3.393249107	\( -\frac{153722875}{3} a + \frac{657508625}{3} \)	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -8593 a - 28141\) , \( 807364 a + 2644048\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8593a-28141\right){x}+807364a+2644048$

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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.