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
51.4-c1	51.4-c	$2$	$2$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	51.4	\( 3 \cdot 17 \)	\( 3^{10} \cdot 17 \)	$0.86100$	$(-a+1), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2 \)	$1$	$2.810507882$	0.389747318	\( \frac{986535013952}{1003833} a - \frac{756768661969}{334611} \)	\( \bigl[1\) , \( a\) , \( a\) , \( 5 a + 1\) , \( 2 a - 2\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+1\right){x}+2a-2$
153.6-c1	153.6-c	$2$	$2$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	153.6	\( 3^{2} \cdot 17 \)	\( 3^{16} \cdot 17 \)	$1.13314$	$(-a+1), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$7.789098936$	2.160307354	\( \frac{986535013952}{1003833} a - \frac{756768661969}{334611} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 15 a - 15\) , \( -27 a + 50\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(15a-15\right){x}-27a+50$
459.2-a1	459.2-a	$2$	$2$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	459.2	\( 3^{3} \cdot 17 \)	\( 3^{16} \cdot 17 \)	$1.49129$	$(-a), (-a+1), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \cdot 5 \)	$1$	$1.808292701$	2.507650791	\( \frac{986535013952}{1003833} a - \frac{756768661969}{334611} \)	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 21 a + 18\) , \( 47 a + 55\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(21a+18\right){x}+47a+55$
867.5-a1	867.5-a	$2$	$2$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	867.5	\( 3 \cdot 17^{2} \)	\( 3^{10} \cdot 17^{7} \)	$1.74830$	$(-a+1), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$3.646430463$	1.011337846	\( \frac{986535013952}{1003833} a - \frac{756768661969}{334611} \)	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 140 a + 135\) , \( 576 a + 860\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(140a+135\right){x}+576a+860$
1377.1-r1	1377.1-r	$2$	$2$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1377.1	\( 3^{4} \cdot 17 \)	\( 3^{22} \cdot 17 \)	$1.96265$	$(-a), (-a+1), (a+4)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.434329674$	$5.011539318$	2.414787726	\( \frac{986535013952}{1003833} a - \frac{756768661969}{334611} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( 45 a\) , \( -11 a + 174\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}+45a{x}-11a+174$

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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.