Elliptic curve search results

Results (3 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
9900.5-k3	9900.5-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	9900.5	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( 2^{8} \cdot 3^{20} \cdot 5^{8} \cdot 11^{2} \)	$2.95627$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	\( 2^{10} \)	$0.229760737$	$0.290729869$	5.155954704	\( -\frac{430679515835908387}{118378482750000} a + \frac{176061193065969059}{19729747125000} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -22 a + 829\) , \( 4807 a - 1323\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a+829\right){x}+4807a-1323$
49500.6-v3	49500.6-v	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.6	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{8} \cdot 3^{20} \cdot 5^{14} \cdot 11^{2} \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{9} \)	$1.610206649$	$0.130018350$	8.079786671	\( -\frac{430679515835908387}{118378482750000} a + \frac{176061193065969059}{19729747125000} \)	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2463 a - 1465\) , \( -40408 a - 49051\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2463a-1465\right){x}-40408a-49051$
49500.7-k3	49500.7-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.7	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{8} \cdot 3^{20} \cdot 5^{14} \cdot 11^{2} \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{11} \cdot 3 \)	$0.130991620$	$0.130018350$	7.887566617	\( -\frac{430679515835908387}{118378482750000} a + \frac{176061193065969059}{19729747125000} \)	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2442 a + 633\) , \( -50026 a + 67587\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2442a+633\right){x}-50026a+67587$

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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.