Elliptic curves over 5.5.70601.1 of conductor 7.1

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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
7.1-a1	7.1-a	$2$	$3$	5.5.70601.1	$5$	$[5, 0]$	7.1	\( 7 \)	\( - 7^{6} \)	$28.84389$	$(-a^4+6a^2+2a-4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 2 \)	$0.032410606$	$1352.120669$	1.64929060	\( -\frac{3986622664}{117649} a^{4} + \frac{2668349896}{117649} a^{3} + \frac{20834045607}{117649} a^{2} - \frac{162996513}{16807} a - \frac{12309440397}{117649} \)	\( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( -a^{4} - a^{3} + 9 a^{2} + 3 a - 3\) , \( -2 a^{3} + 4 a^{2} + 2 a - 1\bigr] \)	${y}^2+\left(2a^{4}-a^{3}-11a^{2}+a+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}^{2}+\left(-a^{4}-a^{3}+9a^{2}+3a-3\right){x}-2a^{3}+4a^{2}+2a-1$
7.1-a2	7.1-a	$2$	$3$	5.5.70601.1	$5$	$[5, 0]$	7.1	\( 7 \)	\( - 7^{2} \)	$28.84389$	$(-a^4+6a^2+2a-4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	\( 2 \)	$0.010803535$	$4056.362009$	1.64929060	\( \frac{392767}{49} a^{4} + \frac{404875}{49} a^{3} - \frac{2995121}{49} a^{2} - \frac{227585}{7} a + \frac{856140}{49} \)	\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 3\) , \( a^{4} - 7 a^{2} + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( 6 a^{4} - 4 a^{3} - 29 a^{2} - 2 a + 20\) , \( 5 a^{4} - a^{3} - 31 a^{2} - 4 a + 22\bigr] \)	${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+4a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-7a^{2}+5\right){x}^{2}+\left(6a^{4}-4a^{3}-29a^{2}-2a+20\right){x}+5a^{4}-a^{3}-31a^{2}-4a+22$

 

  *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.