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
51.2-a5 51.2-a $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
51.2
\( 3 \cdot 17 \)
\( 3^{4} \cdot 17 \)
$1.54873$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$188.9858566$
0.656200891
\( -\frac{97672967}{153} a^{2} + \frac{40445950}{153} a + \frac{269027197}{153} \)
\( \bigl[a^{2} - 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 10 a^{2} - 4 a - 29\) , \( -15 a^{2} + 4 a + 41\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(10a^{2}-4a-29\right){x}-15a^{2}+4a+41$
153.1-b4 153.1-b $6$
$8$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( 3^{10} \cdot 17 \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2 \)
$1$
$17.44502313$
0.969167952
\( -\frac{97672967}{153} a^{2} + \frac{40445950}{153} a + \frac{269027197}{153} \)
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 1\) , \( a^{2} - 6\) , \( a - 6\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(a^{2}-6\right){x}+a-6$
Download
displayed columns for
to
Text
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.
