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-a5	24.1-a	$6$	$8$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 11^{12} \)	$2.98647$	$(2,a+1), (3,a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$12.50076067$	$3.635347017$	6.019284716	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 261 a - 24\) , \( 2158 a + 24154\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(261a-24\right){x}+2158a+24154$
24.1-b5	24.1-b	$6$	$8$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 11^{12} \)	$2.98647$	$(2,a+1), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1$	$3.635347017$	0.963026950	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 253 a - 61\) , \( -4476 a - 23267\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(253a-61\right){x}-4476a-23267$
24.1-c5	24.1-c	$6$	$8$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$2.98647$	$(2,a+1), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$3.635347017$	1.926053901	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)	${y}^2={x}^3+{x}^2-64{x}-220$
24.1-d5	24.1-d	$6$	$8$	\(\Q(\sqrt{-57}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$2.98647$	$(2,a+1), (3,a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$17.52890723$	$3.635347017$	4.220202522	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)	${y}^2={x}^3-{x}^2-64{x}+220$

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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.