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	$6$	$8$	\(\Q(\sqrt{6}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \)	$0.96894$	$(-a+2), (a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1$	$5.683508517$	1.160141318	\( \frac{207646}{6561} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 1\) , \( 21\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+{x}+21$
24.1-b1	24.1-b	$6$	$8$	\(\Q(\sqrt{6}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \)	$0.96894$	$(-a+2), (a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1.079273864$	$2.325279868$	1.024545539	\( \frac{207646}{6561} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -78 a + 194\) , \( 4376 a - 10718\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-78a+194\right){x}+4376a-10718$
48.1-a1	48.1-a	$6$	$8$	\(\Q(\sqrt{6}) \)	$2$	$[2, 0]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \)	$1.15227$	$(-a+2), (a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{6} \)	$1$	$2.325279868$	1.898583062	\( \frac{207646}{6561} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 6\) , \( -18\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+6{x}-18$
48.1-b1	48.1-b	$6$	$8$	\(\Q(\sqrt{6}) \)	$2$	$[2, 0]$	48.1	\( 2^{4} \cdot 3 \)	\( 2^{10} \cdot 3^{16} \)	$1.15227$	$(-a+2), (a+3)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{6} \)	$1$	$5.683508517$	1.160141318	\( \frac{207646}{6561} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -80 a + 193\) , \( -4455 a + 10911\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-80a+193\right){x}-4455a+10911$

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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.