Elliptic curve search results

Results (8 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
15.1-a1	15.1-a	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{2} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$7.392952009$	$0.558925428$	3.226020275	\( -\frac{147281603041}{215233605} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -5091\) , \( -237810\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-5091{x}-237810$
15.1-b1	15.1-b	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1$	$0.558925428$	0.872728585	\( -\frac{147281603041}{215233605} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
15.1-c1	15.1-c	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{2} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{6} \)	$1.654699577$	$0.558925428$	5.776414488	\( -\frac{147281603041}{215233605} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -5391\) , \( 285606\bigr] \)	${y}^2+{x}{y}={x}^3-5391{x}+285606$
15.1-d1	15.1-d	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{6} \)	$2.617916422$	$0.558925428$	4.569460994	\( -\frac{147281603041}{215233605} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 155\) , \( 1190\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+155{x}+1190$
15.1-e1	15.1-e	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{44} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$5.201251375$	$0.558925428$	2.269640378	\( -\frac{147281603041}{215233605} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( -708\) , \( -14497\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-708{x}-14497$
15.1-f1	15.1-f	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{14} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$64$	\( 2^{2} \)	$1$	$0.558925428$	3.490914343	\( -\frac{147281603041}{215233605} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2503\) , \( 128482\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-2503{x}+128482$
15.1-g1	15.1-g	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{44} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{6} \)	$1$	$0.558925428$	3.490914343	\( -\frac{147281603041}{215233605} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-990{x}+22765$
15.1-h1	15.1-h	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{32} \cdot 5^{14} \)	$3.60401$	$(3,a), (5,a)$	$0 \le r \le 1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs		\( 2^{6} \)	$1$	$0.558925428$	7.733633321	\( -\frac{147281603041}{215233605} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-2751{x}-104477$

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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.