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	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$4.49279$	$(2,a+1), (3,a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$16.62854488$	$7.270694035$	2.661186243	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)	${y}^2={x}^3-{x}^2-64{x}+220$
24.1-b5	24.1-b	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 23^{12} \)	$4.49279$	$(2,a+1), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1$	$7.270694035$	0.640148915	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 633 a - 4049\) , \( -33908 a + 36669\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(633a-4049\right){x}-33908a+36669$
24.1-c5	24.1-c	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$4.49279$	$(2,a+1), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$7.270694035$	1.280297830	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)	${y}^2={x}^3+{x}^2-64{x}-220$
24.1-d5	24.1-d	$6$	$8$	\(\Q(\sqrt{-129}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 23^{12} \)	$4.49279$	$(2,a+1), (3,a)$	$0 \le r \le 1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs		\( 2^{3} \)	$1$	$7.270694035$	11.39152378	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 653 a - 3964\) , \( 20394 a + 52802\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(653a-3964\right){x}+20394a+52802$

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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.