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
17.1-a4	17.1-a	$4$	$4$	3.3.148.1	$3$	$[3, 0]$	17.1	\( 17 \)	\( 17 \)	$1.74319$	$(2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 1 \)	$1$	$108.3610925$	0.556701683	\( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \)	\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( -2 a^{2} + a + 6\) , \( -3 a^{2} + 2 a + 9\bigr] \)	${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{2}+a+6\right){x}-3a^{2}+2a+9$
272.1-d4	272.1-d	$4$	$4$	3.3.148.1	$3$	$[3, 0]$	272.1	\( 2^{4} \cdot 17 \)	\( 2^{12} \cdot 17 \)	$2.76714$	$(a^2-a-2), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.042462846$	$189.5008899$	1.984315634	\( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \)	\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( -1\) , \( -a^{2} + a + 3\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}-{x}-a^{2}+a+3$
289.2-a4	289.2-a	$4$	$4$	3.3.148.1	$3$	$[3, 0]$	289.2	\( 17^{2} \)	\( 17^{7} \)	$2.79524$	$(2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.528516232$	$39.91560735$	1.300563250	\( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \)	\( \bigl[1\) , \( 0\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 8 a^{2} - 6 a - 27\bigr] \)	${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}+8a^{2}-6a-27$
425.2-b4	425.2-b	$4$	$4$	3.3.148.1	$3$	$[3, 0]$	425.2	\( 5^{2} \cdot 17 \)	\( 5^{6} \cdot 17 \)	$2.98081$	$(a^2-a-1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$37.92057115$	1.558525873	\( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \)	\( \bigl[1\) , \( -a^{2} + 1\) , \( a\) , \( a\) , \( -a\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+a{x}-a$

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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.