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
9.1-a1 9.1-a $1$
$1$
4.4.19429.1 $4$
$[4, 0]$
9.1
\( 3^{2} \)
\( 3^{19} \)
$16.39246$
$(a^3-a^2-6a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2^{2} \)
$0.395646413$
$86.81605376$
3.942775354
\( -\frac{554873342}{1594323} a^{3} + \frac{311661553}{531441} a^{2} + \frac{2398493765}{1594323} a + \frac{609744973}{1594323} \)
\( \bigl[a^{3} - a^{2} - 5 a - 2\) , \( -a\) , \( a\) , \( -4 a^{3} + 5 a^{2} + 20 a + 8\) , \( -59 a^{3} + 126 a^{2} + 261 a - 228\bigr] \) ${y}^2+\left(a^{3}-a^{2}-5a-2\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-4a^{3}+5a^{2}+20a+8\right){x}-59a^{3}+126a^{2}+261a-228$
9.1-b1 9.1-b $1$
$1$
4.4.19429.1 $4$
$[4, 0]$
9.1
\( 3^{2} \)
\( 3^{9} \)
$16.39246$
$(a^3-a^2-6a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2^{2} \)
$0.075320738$
$350.0394464$
3.026399907
\( -\frac{46448}{27} a^{3} - \frac{6578}{9} a^{2} + \frac{120947}{27} a - \frac{52073}{27} \)
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( a^{3} - 3 a^{2} + 10\) , \( -a^{3} + 5 a^{2} - 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{3}-3a^{2}+10\right){x}-a^{3}+5a^{2}-11$
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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.
