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
17856.2-a3
17856.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
17856.2
\( 2^{6} \cdot 3^{2} \cdot 31 \)
\( 2^{20} \cdot 3^{7} \cdot 31^{4} \)
$1.78914$
$(-2a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.724272481$
1.672635649
\( -\frac{2499774004}{2770563} a + \frac{4015907912}{2770563} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 41 a + 53\) , \( 337 a - 100\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(41a+53\right){x}+337a-100$
23808.2-a3
23808.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
23808.2
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{20} \cdot 3 \cdot 31^{4} \)
$1.92256$
$(-2a+1), (6a-5), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.254476736$
1.448544963
\( -\frac{2499774004}{2770563} a + \frac{4015907912}{2770563} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a - 18\) , \( -a - 49\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-13a-18\right){x}-a-49$
23808.2-b3
23808.2-b
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
23808.2
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{20} \cdot 3 \cdot 31^{4} \)
$1.92256$
$(-2a+1), (6a-5), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.240179320$
$1.254476736$
3.592911016
\( -\frac{2499774004}{2770563} a + \frac{4015907912}{2770563} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 31 a - 13\) , \( a + 49\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(31a-13\right){x}+a+49$
71424.2-f3
71424.2-f
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
71424.2
\( 2^{8} \cdot 3^{2} \cdot 31 \)
\( 2^{20} \cdot 3^{7} \cdot 31^{4} \)
$2.53023$
$(-2a+1), (6a-5), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.724272481$
1.672635649
\( -\frac{2499774004}{2770563} a + \frac{4015907912}{2770563} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 54 a - 93\) , \( -297 a + 153\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(54a-93\right){x}-297a+153$
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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.