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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
44.3-b2	44.3-b	$2$	$5$	4.4.8000.1	$4$	$[4, 0]$	44.3	\( 2^{2} \cdot 11 \)	\( 2^{20} \cdot 11^{5} \)	$12.82671$	$(a+1), (a^2+a-4)$	$0 \le r \le 1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.4[2]		\( 2 \cdot 5 \)	$1$	$0.401031874$	3.181808836	\( \frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} - \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \)	\( \bigl[\frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( 34 a^{3} + \frac{45}{2} a^{2} - 167 a - 378\) , \( -\frac{1153}{2} a^{3} + \frac{4693}{2} a^{2} + 1106 a - 8757\bigr] \)	${y}^2+\left(\frac{1}{2}a^{2}+a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}^{2}+\left(34a^{3}+\frac{45}{2}a^{2}-167a-378\right){x}-\frac{1153}{2}a^{3}+\frac{4693}{2}a^{2}+1106a-8757$
44.3-c1	44.3-c	$2$	$5$	4.4.8000.1	$4$	$[4, 0]$	44.3	\( 2^{2} \cdot 11 \)	\( 2^{20} \cdot 11^{5} \)	$12.82671$	$(a+1), (a^2+a-4)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.1[2]	$1$	\( 2 \cdot 5^{2} \)	$1$	$78.70372532$	1.759868799	\( \frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} - \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \)	\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{2} - a - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -\frac{725}{2} a^{3} + 84 a^{2} + 2093 a - 2043\) , \( \frac{16043}{2} a^{3} - \frac{6019}{2} a^{2} - 47418 a + 50295\bigr] \)	${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-4\right){x}^{2}+\left(-\frac{725}{2}a^{3}+84a^{2}+2093a-2043\right){x}+\frac{16043}{2}a^{3}-\frac{6019}{2}a^{2}-47418a+50295$

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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.