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
24.1-a2	24.1-a	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \)	$2.16662$	$(2,a), (3,a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$1$	$7.270694035$	1.327441044	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3-{x}^2+{x}$
24.1-b2	24.1-b	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{14} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$2.249823046$	$7.270694035$	2.986507453	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \)	${y}^2={x}^3+6{x}-7$
24.1-c2	24.1-c	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 5^{12} \)	$2.16662$	$(2,a), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1$	$7.270694035$	2.654882088	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \)	${y}^2={x}^3+{x}^2+17{x}+38$
24.1-d2	24.1-d	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$1.665930347$	$7.270694035$	4.422848640	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \)	${y}^2={x}^3+{x}^2+3{x}+3$
48.1-a2	48.1-a	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \cdot 5^{12} \)	$2.57656$	$(2,a), (3,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$1.615637236$	$7.270694035$	4.289326359	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 17\) , \( -38\bigr] \)	${y}^2={x}^3-{x}^2+17{x}-38$
48.1-b2	48.1-b	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$2.57656$	$(2,a), (3,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2 \)	$1$	$7.270694035$	2.654882088	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \)	${y}^2={x}^3-{x}^2+3{x}-3$
48.1-c2	48.1-c	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \)	$2.57656$	$(2,a), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$2.841664688$	$7.270694035$	3.772142340	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3+{x}^2+{x}$
48.1-d2	48.1-d	$6$	$8$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{8} \cdot 3^{14} \)	$2.57656$	$(2,a), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2 \)	$4.274166887$	$7.270694035$	5.673704555	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)	${y}^2={x}^3+6{x}+7$

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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.