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
8.1-a2 8.1-a $2$
$3$
\(\Q(\sqrt{241}) \) $2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{14} \)
$2.33303$
$(-393a-2854), (393a-3247)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B $1$
\( 2 \cdot 3 \)
$1$
$17.50871291$
6.767012065
\( \frac{615}{64} a + \frac{3917}{16} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2879460343066 a + 23790352869908\) , \( -22072265823414034036 a + 182362988204191549224\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2879460343066a+23790352869908\right){x}-22072265823414034036a+182362988204191549224$
32.4-b2 32.4-b $2$
$3$
\(\Q(\sqrt{241}) \) $2$
$[2, 0]$
32.4
\( 2^{5} \)
\( 2^{14} \)
$3.29940$
$(-393a-2854), (393a-3247)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B $1$
\( 2 \)
$1.106754909$
$12.14356657$
3.462973634
\( \frac{615}{64} a + \frac{3917}{16} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 24 a + 156\) , \( 270 a + 1952\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a+156\right){x}+270a+1952$
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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.
