Elliptic curves over 5.5.70601.1 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	$2$	$7$	5.5.70601.1	$5$	$[5, 0]$	29.1	\( 29 \)	\( 29^{7} \)	$33.24940$	$(2a^4-2a^3-9a^2+2a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$7$	7B.1.3	$49$	\( 7 \)	$1$	$0.610692715$	0.788336134	\( \frac{1499741787190786782165925}{17249876309} a^{4} - \frac{4214003745944059872006099}{17249876309} a^{3} + \frac{74873005092991374350620}{17249876309} a^{2} + \frac{2994939658199456178076242}{17249876309} a - \frac{879336253518581869182340}{17249876309} \)	\( \bigl[a^{4} - 6 a^{2} - a + 3\) , \( -a^{4} + 7 a^{2} + a - 6\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( 27 a^{4} + 49 a^{3} - 206 a^{2} - 213 a - 28\) , \( 2022 a^{4} + 73 a^{3} - 11190 a^{2} - 5360 a + 2507\bigr] \)	${y}^2+\left(a^{4}-6a^{2}-a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+7a^{2}+a-6\right){x}^{2}+\left(27a^{4}+49a^{3}-206a^{2}-213a-28\right){x}+2022a^{4}+73a^{3}-11190a^{2}-5360a+2507$
29.1-a2	29.1-a	$2$	$7$	5.5.70601.1	$5$	$[5, 0]$	29.1	\( 29 \)	\( 29 \)	$33.24940$	$(2a^4-2a^3-9a^2+2a+3)$	0	$\Z/7\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$7$	7B.1.1	$1$	\( 1 \)	$1$	$10263.91246$	0.788336134	\( \frac{455575}{29} a^{4} - \frac{100246}{29} a^{3} - \frac{2321756}{29} a^{2} - \frac{953052}{29} a + \frac{566128}{29} \)	\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 1\) , \( a^{4} - 6 a^{2} - 3 a + 2\bigr] \)	${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}+3\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+2a+1\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+6a+1\right){x}+a^{4}-6a^{2}-3a+2$

 

  *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.