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-a3	24.1-a	$6$	$8$	\(\Q(\sqrt{-69}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{4} \cdot 3^{4} \cdot 13^{12} \)	$3.28584$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$3.035150282$	$7.270694035$	5.313265514	\( \frac{35152}{9} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 27 a + 46\) , \( -49 a + 654\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(27a+46\right){x}-49a+654$
24.1-b3	24.1-b	$6$	$8$	\(\Q(\sqrt{-69}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{4} \cdot 3^{4} \cdot 13^{12} \)	$3.28584$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$8.682821893$	$7.270694035$	7.599975922	\( \frac{35152}{9} \)	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 15 a + 91\) , \( -188 a - 538\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(15a+91\right){x}-188a-538$
24.1-c3	24.1-c	$6$	$8$	\(\Q(\sqrt{-69}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{16} \cdot 3^{4} \)	$3.28584$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$5.040044010$	$7.270694035$	4.411493590	\( \frac{35152}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \)	${y}^2={x}^3+{x}^2-4{x}-4$
24.1-d3	24.1-d	$6$	$8$	\(\Q(\sqrt{-69}) \)	$2$	$[0, 1]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{16} \cdot 3^{4} \)	$3.28584$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$4.499274317$	$7.270694035$	1.969081993	\( \frac{35152}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)	${y}^2={x}^3-{x}^2-4{x}+4$

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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.