Elliptic curves over 5.5.70601.1 of conductor 17.1

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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
17.1-a1	17.1-a	$2$	$3$	5.5.70601.1	$5$	$[5, 0]$	17.1	\( 17 \)	\( - 17^{3} \)	$31.52019$	$(-a^2+2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 1 \)	$0.125400656$	$962.3659708$	2.27093470	\( \frac{293778407}{289} a^{4} - \frac{543407845}{289} a^{3} - \frac{1007035812}{289} a^{2} + \frac{1443156771}{289} a - \frac{345466559}{289} \)	\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -a^{4} + 6 a^{2} + 3 a - 3\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 6\) , \( -3 a^{4} + 2 a^{3} + 14 a^{2} + 3 a - 6\) , \( -5 a^{4} + 5 a^{3} + 22 a^{2} - 2 a - 14\bigr] \)	${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(3a^{4}-2a^{3}-15a^{2}+a+6\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+3a-3\right){x}^{2}+\left(-3a^{4}+2a^{3}+14a^{2}+3a-6\right){x}-5a^{4}+5a^{3}+22a^{2}-2a-14$
17.1-a2	17.1-a	$2$	$3$	5.5.70601.1	$5$	$[5, 0]$	17.1	\( 17 \)	\( -17 \)	$31.52019$	$(-a^2+2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 1 \)	$0.041800218$	$2887.097912$	2.27093470	\( -\frac{541923}{17} a^{4} - \frac{814933}{17} a^{3} + \frac{667123}{17} a^{2} + \frac{563417}{17} a - \frac{220652}{17} \)	\( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( -a^{4} + 6 a^{2} + a - 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 2\) , \( -6 a^{4} + a^{3} + 36 a^{2} + 6 a - 21\) , \( 24 a^{4} - 19 a^{3} - 121 a^{2} + 15 a + 71\bigr] \)	${y}^2+\left(2a^{4}-a^{3}-10a^{2}+3\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-2\right){x}^{2}+\left(-6a^{4}+a^{3}+36a^{2}+6a-21\right){x}+24a^{4}-19a^{3}-121a^{2}+15a+71$

 

  *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.