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
27.1-a1
27.1-a
$2$
$13$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
27.1
\( 3^{3} \)
\( - 3^{39} \)
$1.08342$
$(3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$13$
13B.1.2
$1$
\( 13 \)
$1$
$0.216755369$
0.402545685
\( -\frac{1713910976512}{1594323} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( 652 a^{2} - 391 a - 1564\) , \( 10528 a^{2} - 5979 a - 24046\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(652a^{2}-391a-1564\right){x}+10528a^{2}-5979a-24046$
729.1-a1
729.1-a
$2$
$13$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
729.1
\( 3^{6} \)
\( - 3^{57} \)
$1.87654$
$(3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$13$
13B.12.2
$1$
\( 2 \)
$1$
$3.604186821$
1.029767663
\( -\frac{1713910976512}{1594323} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 5865 a^{2} - 3519 a - 14076\) , \( -286610 a^{2} + 163777 a + 655108\bigr] \)
${y}^2+a{y}={x}^{3}+\left(5865a^{2}-3519a-14076\right){x}-286610a^{2}+163777a+655108$
1323.1-b1
1323.1-b
$2$
$13$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1323.1
\( 3^{3} \cdot 7^{2} \)
\( - 3^{39} \cdot 7^{6} \)
$2.07251$
$(-a^2-a+2), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$13$
13B.12.2
$1$
\( 1 \)
$1$
$7.078482397$
1.011211771
\( -\frac{1713910976512}{1594323} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -912\) , \( 10919\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-912{x}+10919$
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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.