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
59.2-a1 59.2-a $2$
$2$
4.4.2225.1 $4$
$[4, 0]$
59.2
\( 59 \)
\( -59 \)
$7.01714$
$(-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$339.4348471$
1.799001091
\( -\frac{80084033}{59} a^{3} - \frac{11844265}{59} a^{2} + \frac{388329966}{59} a + \frac{284613459}{59} \)
\( \bigl[a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\) , \( a + 1\) , \( -a^{3} + a^{2} + a + 1\) , \( \frac{3}{2} a^{3} - \frac{9}{2} a^{2} - \frac{1}{2} a + 3\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+2\right){x}^{2}+\left(-a^{3}+a^{2}+a+1\right){x}+\frac{3}{2}a^{3}-\frac{9}{2}a^{2}-\frac{1}{2}a+3$
59.2-a2 59.2-a $2$
$2$
4.4.2225.1 $4$
$[4, 0]$
59.2
\( 59 \)
\( - 59^{2} \)
$7.01714$
$(-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$169.7174235$
1.799001091
\( -\frac{9431597}{3481} a^{3} + \frac{30375282}{3481} a^{2} - \frac{4325613}{3481} a - \frac{29186969}{3481} \)
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 1\) , \( a^{2} - a - 2\) , \( -a^{2} + 4\) , \( -11 a^{3} + 20 a^{2} + 39 a - 55\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-1\right){x}^{2}+\left(-a^{2}+4\right){x}-11a^{3}+20a^{2}+39a-55$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
