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
10.1-g1 10.1-g $1$
$1$
3.3.1620.1 $3$
$[3, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{15} \cdot 5 \)
$5.27913$
$(a+2), (2a^2-3a-19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$1$
$23.62561048$
0.586983011
\( \frac{5821540049}{160} a^{2} - \frac{506086881}{10} a - \frac{58596354789}{160} \)
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 8\) , \( a + 1\) , \( 10 a^{2} - 12 a - 85\) , \( 27 a^{2} - 31 a - 264\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+8\right){x}^{2}+\left(10a^{2}-12a-85\right){x}+27a^{2}-31a-264$
50.3-d1 50.3-d $1$
$1$
3.3.1620.1 $3$
$[3, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( - 2^{15} \cdot 5^{7} \)
$6.90332$
$(a+2), (2a^2-3a-19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \cdot 3 \cdot 5 \)
$1$
$10.56569421$
7.875203495
\( \frac{5821540049}{160} a^{2} - \frac{506086881}{10} a - \frac{58596354789}{160} \)
\( \bigl[1\) , \( -a^{2} + 3 a + 8\) , \( a^{2} - a - 8\) , \( 167 a^{2} - 391 a - 1050\) , \( 2162 a^{2} - 5308 a - 12688\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-8\right){y}={x}^{3}+\left(-a^{2}+3a+8\right){x}^{2}+\left(167a^{2}-391a-1050\right){x}+2162a^{2}-5308a-12688$
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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.
