Elliptic curve search results

Results (6 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
361.1-a2	361.1-a	$3$	$9$	\(\Q(\sqrt{-39}) \)	$2$	$[0, 1]$	361.1	\( 19^{2} \)	\( 3^{12} \cdot 19^{6} \)	$2.43247$	$(19)$	$2$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 3 \)	$1.228183505$	$2.805927025$	1.471553517	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -84\) , \( 315\bigr] \)	${y}^2+{y}={x}^3-84{x}+315$
361.2-b2	361.2-b	$3$	$9$	\(\Q(\sqrt{-13}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 19^{6} \)	$2.80878$	$(19,a+5), (19,a+14)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 1 \)	$1.811745694$	$2.805927025$	2.819888454	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( -1\) , \( a\) , \( -9\) , \( 18\bigr] \)	${y}^2+a{y}={x}^3-{x}^2-9{x}+18$
361.2-a2	361.2-a	$3$	$9$	\(\Q(\sqrt{-91}) \)	$2$	$[0, 1]$	361.2	\( 19^{2} \)	\( 5^{12} \cdot 19^{6} \)	$3.71566$	$(19,a+8), (19,a+10)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 1 \)	$1.811745694$	$2.805927025$	2.131635307	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -27 a + 198\) , \( 236 a + 1342\bigr] \)	${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(-27a+198\right){x}+236a+1342$
361.1-b2	361.1-b	$3$	$9$	\(\Q(\sqrt{-26}) \)	$2$	$[0, 1]$	361.1	\( 19^{2} \)	\( 2^{12} \cdot 19^{6} \)	$3.97221$	$(19)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 3 \)	$0.359875702$	$2.805927025$	2.376421484	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -37\) , \( 81\bigr] \)	${y}^2={x}^3+{x}^2-37{x}+81$
19.1-a2	19.1-a	$3$	$9$	\(\Q(\sqrt{-247}) \)	$2$	$[0, 1]$	19.1	\( 19 \)	\( 13^{12} \cdot 19^{6} \)	$2.93208$	$(19,a+9)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	\( 2 \)	$1.811745694$	$2.805927025$	2.587707116	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -1577\) , \( -26178\bigr] \)	${y}^2+{y}={x}^3+{x}^2-1577{x}-26178$
361.1-a2	361.1-a	$3$	$9$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	361.1	\( 19^{2} \)	\( 19^{6} \)	$1.40439$	$(19)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 3 \)	$1.811745694$	$1.848946532$	0.619382107	\( -\frac{89915392}{6859} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$

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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.