Elliptic curves over 5.5.24217.1 of conductor 85.2

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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
85.2-a1	85.2-a	$2$	$2$	5.5.24217.1	$5$	$[5, 0]$	85.2	$5 \cdot 17$	$5^{2} \cdot 17$	$21.68406$	$(2a^4-a^3-9a^2+2a+3), (a^2-a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$346.8383044$	1.11438918	$-\frac{62677552}{425} a^{4} + \frac{90221181}{425} a^{3} + \frac{148784492}{425} a^{2} - \frac{70726799}{425} a - \frac{76071034}{425}$	$\bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4$ , $3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7$ , $0$ , $2 a^{4} - a^{3} - 9 a^{2} + 3 a + 6$ , $0\bigr]$	${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){x}{y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+5a+7\right){x}^{2}+\left(2a^{4}-a^{3}-9a^{2}+3a+6\right){x}$
85.2-a2	85.2-a	$2$	$2$	5.5.24217.1	$5$	$[5, 0]$	85.2	$5 \cdot 17$	$5 \cdot 17^{2}$	$21.68406$	$(2a^4-a^3-9a^2+2a+3), (a^2-a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$346.8383044$	1.11438918	$\frac{332100987110154}{1445} a^{4} - \frac{641864431345097}{1445} a^{3} - \frac{405783721341489}{1445} a^{2} + \frac{419172695961983}{1445} a + \frac{181943957339298}{1445}$	$\bigl[2 a^{4} - a^{3} - 9 a^{2} + 4 a + 4$ , $3 a^{4} - 2 a^{3} - 14 a^{2} + 5 a + 7$ , $0$ , $-8 a^{4} + 4 a^{3} + 36 a^{2} - 12 a - 24$ , $-34 a^{4} + 13 a^{3} + 154 a^{2} - 33 a - 90\bigr]$	${y}^2+\left(2a^{4}-a^{3}-9a^{2}+4a+4\right){x}{y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+5a+7\right){x}^{2}+\left(-8a^{4}+4a^{3}+36a^{2}-12a-24\right){x}-34a^{4}+13a^{3}+154a^{2}-33a-90$
85.2-b1	85.2-b	$2$	$2$	5.5.24217.1	$5$	$[5, 0]$	85.2	$5 \cdot 17$	$5^{2} \cdot 17$	$21.68406$	$(2a^4-a^3-9a^2+2a+3), (a^2-a-3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$0.007549410$	$16285.02719$	1.97506496	$-\frac{102640958}{425} a^{4} + \frac{58128349}{425} a^{3} + \frac{509229993}{425} a^{2} - \frac{171001971}{425} a - \frac{338930961}{425}$	$\bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2$ , $-3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6$ , $a^{4} - a^{3} - 4 a^{2} + 4 a + 2$ , $5 a^{4} - 4 a^{3} - 23 a^{2} + 11 a + 7$ , $8 a^{4} - 5 a^{3} - 37 a^{2} + 14 a + 14\bigr]$	${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-3a-6\right){x}^{2}+\left(5a^{4}-4a^{3}-23a^{2}+11a+7\right){x}+8a^{4}-5a^{3}-37a^{2}+14a+14$
85.2-b2	85.2-b	$2$	$2$	5.5.24217.1	$5$	$[5, 0]$	85.2	$5 \cdot 17$	$- 5 \cdot 17^{2}$	$21.68406$	$(2a^4-a^3-9a^2+2a+3), (a^2-a-3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$0.015098821$	$8142.513599$	1.97506496	$\frac{185066934807448}{1445} a^{4} - \frac{87464764407119}{1445} a^{3} - \frac{909727616081443}{1445} a^{2} + \frac{231799410298786}{1445} a + \frac{559295724774971}{1445}$	$\bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2$ , $-3 a^{4} + a^{3} + 14 a^{2} - 3 a - 6$ , $a^{4} - a^{3} - 4 a^{2} + 4 a + 2$ , $-50 a^{4} + 26 a^{3} + 232 a^{2} - 74 a - 103$ , $65 a^{4} - 10 a^{3} - 330 a^{2} - 4 a + 225\bigr]$	${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-3a^{4}+a^{3}+14a^{2}-3a-6\right){x}^{2}+\left(-50a^{4}+26a^{3}+232a^{2}-74a-103\right){x}+65a^{4}-10a^{3}-330a^{2}-4a+225$

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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.