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
7.3-a2
7.3-a
$2$
$3$
4.4.13888.1
$4$
$[4, 0]$
7.3
\( 7 \)
\( -7 \)
$13.43061$
$(-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$223.0004007$
1.892281700
\( \frac{138334576381}{21} a^{3} - \frac{401776485356}{21} a^{2} - \frac{604938667369}{21} a + \frac{458963405296}{7} \)
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a\) , \( a\) , \( -\frac{2}{3} a^{3} + \frac{4}{3} a^{2} + \frac{14}{3} a - 3\) , \( -2 a^{3} + a^{2} + 8 a - 4\bigr] \)
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{4}{3}a^{2}+\frac{14}{3}a-3\right){x}-2a^{3}+a^{2}+8a-4$
7.3-b2
7.3-b
$2$
$3$
4.4.13888.1
$4$
$[4, 0]$
7.3
\( 7 \)
\( -7 \)
$13.43061$
$(-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.038231493$
$2178.566117$
2.827041244
\( \frac{138334576381}{21} a^{3} - \frac{401776485356}{21} a^{2} - \frac{604938667369}{21} a + \frac{458963405296}{7} \)
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( -3 a^{3} + 6 a^{2} + 17 a - 18\) , \( \frac{5}{3} a^{3} - \frac{16}{3} a^{2} - \frac{29}{3} a + 28\bigr] \)
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-3a^{3}+6a^{2}+17a-18\right){x}+\frac{5}{3}a^{3}-\frac{16}{3}a^{2}-\frac{29}{3}a+28$
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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.