Elliptic curves over 6.6.703493.1 of conductor 13.2

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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
13.2-a1	13.2-a	$1$	$1$	6.6.703493.1	$6$	$[6, 0]$	13.2	\( 13 \)	\( 13^{7} \)	$92.81049$	$(-a^5+a^4+5a^3-5a^2-3a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$1$	$1063.531897$	1.26800	\( \frac{255013799509031}{62748517} a^{5} - \frac{477311078347916}{62748517} a^{4} - \frac{1339962421221462}{62748517} a^{3} + \frac{2643361615369126}{62748517} a^{2} + \frac{858722677391412}{62748517} a - \frac{2230501197703405}{62748517} \)	\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 6 a^{2} + 11 a - 2\) , \( -a - 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a\) , \( 3 a^{5} + 4 a^{4} - 9 a^{3} - 7 a^{2} + 4 a\) , \( 23 a^{5} + 2 a^{4} - 113 a^{3} + 25 a^{2} + 99 a - 12\bigr] \)	${y}^2+\left(2a^{5}-a^{4}-11a^{3}+6a^{2}+11a-2\right){x}{y}+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a^{5}+4a^{4}-9a^{3}-7a^{2}+4a\right){x}+23a^{5}+2a^{4}-113a^{3}+25a^{2}+99a-12$
13.2-b1	13.2-b	$1$	$1$	6.6.703493.1	$6$	$[6, 0]$	13.2	\( 13 \)	\( - 13^{7} \)	$92.81049$	$(-a^5+a^4+5a^3-5a^2-3a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 7 \)	$0.002349118$	$17461.84080$	2.05407	\( -\frac{379829569709}{62748517} a^{5} + \frac{185472136849}{62748517} a^{4} + \frac{2177940852778}{62748517} a^{3} - \frac{883264147970}{62748517} a^{2} - \frac{2091604847718}{62748517} a + \frac{253378952210}{62748517} \)	\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 10 a - 1\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a - 2\) , \( a^{2} - 2\) , \( 4 a^{5} - 2 a^{4} - 22 a^{3} + 10 a^{2} + 19 a + 2\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 8 a^{2} - 23 a + 1\bigr] \)	${y}^2+\left(2a^{5}-a^{4}-11a^{3}+5a^{2}+10a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-11a-2\right){x}^{2}+\left(4a^{5}-2a^{4}-22a^{3}+10a^{2}+19a+2\right){x}-3a^{5}+2a^{4}+19a^{3}-8a^{2}-23a+1$

 

  *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.