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
121.1-d2	121.1-d	$4$	$22$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( - 11^{3} \)	$1.70252$	$(-4a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 11$	2B, 11B.1.6	$1$	\( 2 \)	$1$	$7.057677431$	0.614291971	\( -357236 a + 1203885 \)	\( \bigl[1\) , \( -a\) , \( a\) , \( -3 a - 4\) , \( -5 a - 13\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3a-4\right){x}-5a-13$
121.1-f2	121.1-f	$4$	$22$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( - 11^{9} \)	$1.70252$	$(-4a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 11$	2B, 11B.10.5	$1$	\( 2 \)	$1$	$4.922210220$	0.428423408	\( -357236 a + 1203885 \)	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 32 a - 106\) , \( 184 a - 613\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-106\right){x}+184a-613$
121.1-h2	121.1-h	$4$	$22$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( - 11^{3} \)	$1.70252$	$(-4a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 11$	2B, 11B.1.5	$1$	\( 2 \)	$1$	$37.76167025$	3.286731521	\( -357236 a + 1203885 \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( 133 a - 448\) , \( -1359 a + 4583\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(133a-448\right){x}-1359a+4583$
121.1-i2	121.1-i	$4$	$22$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( - 11^{9} \)	$1.70252$	$(-4a-9)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 11$	2B, 11B.10.5	$1$	\( 2 \)	$1$	$4.922210220$	0.428423408	\( -357236 a + 1203885 \)	\( \bigl[1\) , \( 0\) , \( a\) , \( -1381 a - 3275\) , \( -83691 a - 198540\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-1381a-3275\right){x}-83691a-198540$

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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.