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-a1	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	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2 \)	$1$	$18.22505448$	1.206983718	\( \frac{625}{3} a + \frac{2125}{3} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2173 a + 9280\) , \( -868440 a + 3712504\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2173a+9280\right){x}-868440a+3712504$
96.6-b1	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	$4$	\( 2 \)	$1$	$12.46322522$	3.301589017	\( \frac{625}{3} a + \frac{2125}{3} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a - 2\) , \( -a - 1\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}-a-1$
192.6-g1	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	\( \frac{625}{3} a + \frac{2125}{3} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 6 a + 30\) , \( 13 a + 49\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a+30\right){x}+13a+49$
192.6-j1	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	\( \frac{625}{3} a + \frac{2125}{3} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -163 a + 704\) , \( 17837 a - 76240\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-163a+704\right){x}+17837a-76240$

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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.