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-a2	121.1-a	$2$	$11$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{8} \)	$1.70252$	$(-4a-9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$11$	11B.1.7	$1$	\( 1 \)	$5.138097620$	$2.776078883$	4.966005310	\( -121 \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( -7\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}-7$
121.1-c2	121.1-c	$2$	$11$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{2} \)	$1.70252$	$(-4a-9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$11$	11B.10.4	$1$	\( 1 \)	$0.207953261$	$18.69052092$	1.353194323	\( -121 \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -a - 2\) , \( 11 a + 26\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+11a+26$
121.1-j2	121.1-j	$2$	$11$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{8} \)	$1.70252$	$(-4a-9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓		✓	$11$	11B.1.4	$1$	\( 3 \)	$0.132762375$	$11.43979716$	1.586308376	\( -121 \)	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 927 a - 3126\) , \( -102858 a + 346862\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(927a-3126\right){x}-102858a+346862$
121.1-k2	121.1-k	$2$	$11$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{2} \)	$1.70252$	$(-4a-9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$11$	11B.10.4	$1$	\( 1 \)	$0.207953261$	$18.69052092$	1.353194323	\( -121 \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3 a - 3\) , \( -9 a + 34\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-3\right){x}-9a+34$

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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.