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-a4	15.1-a	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{8} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1.848238002$	$2.235701712$	3.226020275	\( \frac{111284641}{50625} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -191\) , \( 1800\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-191{x}+1800$
15.1-b4	15.1-b	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{8} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{4} \)	$1$	$2.235701712$	0.872728585	\( \frac{111284641}{50625} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
15.1-c4	15.1-c	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{8} \cdot 7^{12} \)	$3.60401$	$(3,a), (5,a)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{4} \)	$1.654699577$	$2.235701712$	5.776414488	\( \frac{111284641}{50625} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -491\) , \( 1896\bigr] \)	${y}^2+{x}{y}={x}^3-491{x}+1896$
15.1-d4	15.1-d	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{8} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{6} \)	$2.617916422$	$2.235701712$	4.569460994	\( \frac{111284641}{50625} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 255\) , \( -480\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+255{x}-480$
15.1-e4	15.1-e	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{20} \cdot 5^{8} \)	$3.60401$	$(3,a), (5,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{2} \)	$1.300312843$	$2.235701712$	2.269640378	\( \frac{111284641}{50625} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( 192\) , \( -7\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+192{x}-7$
15.1-f4	15.1-f	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{20} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{4} \)	$1$	$2.235701712$	3.490914343	\( \frac{111284641}{50625} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -3\) , \( 2232\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2-3{x}+2232$
15.1-g4	15.1-g	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{20} \cdot 5^{8} \)	$3.60401$	$(3,a), (5,a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$16$	\( 2^{4} \)	$1$	$2.235701712$	3.490914343	\( \frac{111284641}{50625} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$
15.1-h4	15.1-h	$8$	$16$	\(\Q(\sqrt{-105}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{20} \)	$3.60401$	$(3,a), (5,a)$	$0 \le r \le 1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs		\( 2^{6} \)	$1$	$2.235701712$	7.733633321	\( \frac{111284641}{50625} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-251{x}-727$

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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.