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-a7	15.1-a	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$1.848238002$	$2.235701712$	3.226020275	\( \frac{56667352321}{15} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -3621\) , \( 129396\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-3621{x}+129396$
15.1-b7	15.1-b	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1$	$2.235701712$	0.872728585	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
15.1-c7	15.1-c	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$2$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$6.618798309$	$2.235701712$	5.776414488	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3921\) , \( -94830\bigr] \)	${y}^2+{x}{y}={x}^3-3921{x}-94830$
15.1-d7	15.1-d	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$0.654479105$	$2.235701712$	4.569460994	\( \frac{56667352321}{15} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 185\) , \( -172\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+185{x}-172$
15.1-e7	15.1-e	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{14} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$1.300312843$	$2.235701712$	2.269640378	\( \frac{56667352321}{15} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( -438\) , \( 13097\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-438{x}+13097$
15.1-f7	15.1-f	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{14} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1$	$2.235701712$	3.490914343	\( \frac{56667352321}{15} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1753\) , \( -17018\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-1753{x}-17018$
15.1-g7	15.1-g	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{14} \cdot 5^{2} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1$	$2.235701712$	3.490914343	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-720{x}-7259$
15.1-h7	15.1-h	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{14} \)	$3.60401$	$(3,a), (5,a)$	$0 \le r \le 1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs		\( 2^{2} \)	$1$	$2.235701712$	7.733633321	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-2001{x}+34273$

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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.