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
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( -7 \)
$0.78273$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 1 \)
$1$
$20.28981932$
0.941931215
\( -\frac{94831363}{7} a + \frac{268859728}{7} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 18\) , \( 12 a - 37\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-18\right){x}+12a-37$
7.1-a2
7.1-a
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( - 7^{5} \)
$0.78273$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 1 \)
$1$
$20.28981932$
0.941931215
\( -\frac{173650213}{16807} a + \frac{583264453}{16807} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}$
7.1-a3
7.1-a
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( - 7^{10} \)
$0.78273$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2 \)
$1$
$10.14490966$
0.941931215
\( \frac{91176666325}{282475249} a + \frac{199910878122}{282475249} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( -a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}-a-1$
7.1-a4
7.1-a
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( - 7^{2} \)
$0.78273$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 2 \)
$1$
$10.14490966$
0.941931215
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a - 28\) , \( 16 a - 33\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-28\right){x}+16a-33$
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*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.