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
24.1-a1	24.1-a	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{22} \cdot 3^{16} \)	$4.49279$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$2.078568110$	$3.635347017$	2.661186243	\( \frac{207646}{6561} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)	${y}^2={x}^3-{x}^2+16{x}-180$
24.1-b1	24.1-b	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \cdot 23^{12} \)	$4.49279$	$(2,a+1), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$3.635347017$	0.640148915	\( \frac{207646}{6561} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -167 a + 1371\) , \( 25242 a - 14271\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-167a+1371\right){x}+25242a-14271$
24.1-c1	24.1-c	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{22} \cdot 3^{16} \)	$4.49279$	$(2,a+1), (3,a)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$16$	\( 2^{5} \)	$1$	$3.635347017$	1.280297830	\( \frac{207646}{6561} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \)	${y}^2={x}^3+{x}^2+16{x}+180$
24.1-d1	24.1-d	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \cdot 23^{12} \)	$4.49279$	$(2,a+1), (3,a)$	$0 \le r \le 1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs		\( 2^{5} \)	$1$	$3.635347017$	11.39152378	\( \frac{207646}{6561} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -147 a + 1456\) , \( -21956 a - 10078\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-147a+1456\right){x}-21956a-10078$

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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.