Elliptic curves over 5.5.24217.1 of conductor 43.1

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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
43.1-a1	43.1-a	$1$	$1$	5.5.24217.1	$5$	$[5, 0]$	43.1	\( 43 \)	\( - 43^{2} \)	$20.25562$	$(3a^4-a^3-14a^2+3a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2 \)	$1$	$87.59890221$	1.12581878	\( \frac{370574018535535}{1849} a^{4} + \frac{325399130060553}{1849} a^{3} - \frac{1567138777154508}{1849} a^{2} - \frac{1746670430584042}{1849} a - \frac{422020411508467}{1849} \)	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( -2 a^{4} + 9 a^{2} + a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( 3 a^{4} - 5 a^{3} - 16 a^{2} + 16 a + 11\) , \( -6 a^{4} + a^{3} + 26 a^{2} - 2 a - 9\bigr] \)	${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){y}={x}^{3}+\left(-2a^{4}+9a^{2}+a-2\right){x}^{2}+\left(3a^{4}-5a^{3}-16a^{2}+16a+11\right){x}-6a^{4}+a^{3}+26a^{2}-2a-9$
43.1-b1	43.1-b	$1$	$1$	5.5.24217.1	$5$	$[5, 0]$	43.1	\( 43 \)	\( - 43^{2} \)	$20.25562$	$(3a^4-a^3-14a^2+3a+6)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 2 \)	$0.001395606$	$16404.26636$	1.47115856	\( -\frac{673276224}{1849} a^{4} + \frac{251558661}{1849} a^{3} + \frac{3275824811}{1849} a^{2} - \frac{548956180}{1849} a - \frac{1829937870}{1849} \)	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( 4 a^{4} - 2 a^{3} - 19 a^{2} + 6 a + 7\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 13 a - 4\) , \( -3 a^{3} - a^{2} + 13 a + 5\bigr] \)	${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){y}={x}^{3}+\left(4a^{4}-2a^{3}-19a^{2}+6a+7\right){x}^{2}+\left(-2a^{4}+3a^{3}+9a^{2}-13a-4\right){x}-3a^{3}-a^{2}+13a+5$

 

  *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.