Elliptic curves over 5.5.65657.1 of conductor 29.1

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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
29.1-a1	29.1-a	$2$	$3$	5.5.65657.1	$5$	$[5, 0]$	29.1	\( 29 \)	\( -29 \)	$32.06409$	$(-2a^4+3a^3+8a^2-7a-4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 1 \)	$0.012463742$	$6352.309501$	1.54493280	\( \frac{12183}{29} a^{4} - \frac{19048}{29} a^{3} - \frac{55150}{29} a^{2} + \frac{66157}{29} a + \frac{70545}{29} \)	\( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 10 a + 8\) , \( a^{2} - a - 1\) , \( 4 a^{4} - 4 a^{3} - 21 a^{2} + 10 a + 22\) , \( 5 a^{4} - 6 a^{3} - 24 a^{2} + 16 a + 21\bigr] \)	${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(3a^{4}-4a^{3}-13a^{2}+10a+8\right){x}^{2}+\left(4a^{4}-4a^{3}-21a^{2}+10a+22\right){x}+5a^{4}-6a^{3}-24a^{2}+16a+21$
29.1-a2	29.1-a	$2$	$3$	5.5.65657.1	$5$	$[5, 0]$	29.1	\( 29 \)	\( - 29^{3} \)	$32.06409$	$(-2a^4+3a^3+8a^2-7a-4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 1 \)	$0.037391226$	$2117.436500$	1.54493280	\( \frac{3112416550238}{24389} a^{4} - \frac{4117133380738}{24389} a^{3} - \frac{14702539245891}{24389} a^{2} + \frac{10904653871054}{24389} a + \frac{14162641194095}{24389} \)	\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( -6 a^{4} + 9 a^{3} + 25 a^{2} - 25 a - 16\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 11 a + 8\bigr] \)	${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{4}+9a^{3}+25a^{2}-25a-16\right){x}+3a^{4}-5a^{3}-12a^{2}+11a+8$

 

  *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.