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
17856.1-b3 17856.1-b $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
17856.1
\( 2^{6} \cdot 3^{2} \cdot 31 \)
\( 2^{16} \cdot 3^{8} \cdot 31^{2} \)
$1.78914$
$(-2a+1), (-6a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$1$
$1.448544963$
1.672635649
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -26 a + 7\) , \( -25 a + 9\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a+7\right){x}-25a+9$
23808.1-a3 23808.1-a $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
23808.1
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{16} \cdot 3^{2} \cdot 31^{2} \)
$1.92256$
$(-2a+1), (-6a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{3} \)
$1$
$2.508953473$
1.448544963
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 7\) , \( -3 a - 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a-7\right){x}-3a-6$
23808.1-b3 23808.1-b $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
23808.1
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{16} \cdot 3^{2} \cdot 31^{2} \)
$1.92256$
$(-2a+1), (-6a+1), (2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$0.620089660$
$2.508953473$
3.592911016
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a - 2\) , \( 3 a + 6\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(9a-2\right){x}+3a+6$
71424.1-d3 71424.1-d $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
71424.1
\( 2^{8} \cdot 3^{2} \cdot 31 \)
\( 2^{16} \cdot 3^{8} \cdot 31^{2} \)
$2.53023$
$(-2a+1), (-6a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$1$
$1.448544963$
1.672635649
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 21 a - 27\) , \( 45 a - 36\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(21a-27\right){x}+45a-36$
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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.
