Elliptic curves over 6.6.703493.1 of conductor 13.1

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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
13.1-a1	13.1-a	$1$	$1$	6.6.703493.1	$6$	$[6, 0]$	13.1	\( 13 \)	\( 13^{7} \)	$92.81049$	$(3a^5-2a^4-17a^3+10a^2+16a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$1$	$1063.531897$	1.26800	\( -\frac{113153543237056}{62748517} a^{5} - \frac{42457887805007}{62748517} a^{4} + \frac{488800883589612}{62748517} a^{3} - \frac{44516784604511}{62748517} a^{2} - \frac{385469849640510}{62748517} a + \frac{44534588204426}{62748517} \)	\( \bigl[3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 17 a - 4\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 2\) , \( 10 a^{5} - 4 a^{4} - 54 a^{3} + 24 a^{2} + 51 a - 5\) , \( 25 a^{5} - 12 a^{4} - 142 a^{3} + 65 a^{2} + 147 a - 17\bigr] \)	${y}^2+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+17a-4\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+7a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+1\right){x}^{2}+\left(10a^{5}-4a^{4}-54a^{3}+24a^{2}+51a-5\right){x}+25a^{5}-12a^{4}-142a^{3}+65a^{2}+147a-17$
13.1-b1	13.1-b	$1$	$1$	6.6.703493.1	$6$	$[6, 0]$	13.1	\( 13 \)	\( - 13^{7} \)	$92.81049$	$(3a^5-2a^4-17a^3+10a^2+16a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 7 \)	$0.002349118$	$17461.84080$	2.05407	\( \frac{33889457777}{62748517} a^{5} - \frac{83113788886}{62748517} a^{4} - \frac{102300181186}{62748517} a^{3} + \frac{371472408155}{62748517} a^{2} - \frac{227617587843}{62748517} a + \frac{15310089083}{62748517} \)	\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 3\) , \( -a^{5} + 7 a^{3} - a^{2} - 9 a + 2\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -a^{5} - a^{4} + 8 a^{3} + 5 a^{2} - 20 a + 6\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 16 a^{2} - a - 2\bigr] \)	${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-3\right){x}{y}+\left(a^{5}-6a^{3}+8a+2\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-a^{2}-9a+2\right){x}^{2}+\left(-a^{5}-a^{4}+8a^{3}+5a^{2}-20a+6\right){x}+2a^{5}-4a^{4}-8a^{3}+16a^{2}-a-2$

 

  *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.