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
57.1-d3	57.1-d	$6$	$8$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	57.1	\( 3 \cdot 19 \)	\( 3^{2} \cdot 19^{2} \)	$1.85372$	$(4a+13), (10a-43)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{2} \)	$1$	$36.19446804$	0.299629650	\( \frac{389017}{57} \)	\( \bigl[1\) , \( -a\) , \( a\) , \( -18372 a - 60161\) , \( 2300500 a + 7533946\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-18372a-60161\right){x}+2300500a+7533946$
57.1-g3	57.1-g	$6$	$8$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	57.1	\( 3 \cdot 19 \)	\( 3^{2} \cdot 19^{2} \)	$1.85372$	$(4a+13), (10a-43)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{2} \)	$3.892773922$	$18.84609635$	4.858622600	\( \frac{389017}{57} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$
171.1-e3	171.1-e	$6$	$8$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	171.1	\( 3^{2} \cdot 19 \)	\( 3^{8} \cdot 19^{2} \)	$2.43964$	$(4a+13), (10a-43)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$15.07895257$	0.998628029	\( \frac{389017}{57} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( -182 a - 593\) , \( -2528 a - 8280\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-182a-593\right){x}-2528a-8280$
171.1-h3	171.1-h	$6$	$8$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	171.1	\( 3^{2} \cdot 19 \)	\( 3^{8} \cdot 19^{2} \)	$2.43964$	$(4a+13), (10a-43)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{3} \)	$1$	$15.07895257$	0.998628029	\( \frac{389017}{57} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 182 a - 775\) , \( 2528 a - 10808\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(182a-775\right){x}+2528a-10808$

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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.