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
5.1-a4 5.1-a $8$
$16$
4.4.19664.1 $4$
$[4, 0]$
5.1
\( 5 \)
\( 5^{8} \)
$15.32307$
$(a^3-2a^2-5a+1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{3} \)
$0.354797042$
$449.7564671$
2.275891063
\( \frac{105329076}{390625} a^{3} - \frac{187575264}{390625} a^{2} - \frac{525009912}{390625} a + \frac{21361121}{390625} \)
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( 0\) , \( a\) , \( 3 a^{3} - 4 a^{2} - 16 a - 6\) , \( -5 a^{3} + 3 a^{2} + 40 a + 19\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+a{y}={x}^{3}+\left(3a^{3}-4a^{2}-16a-6\right){x}-5a^{3}+3a^{2}+40a+19$
5.1-b5 5.1-b $8$
$16$
4.4.19664.1 $4$
$[4, 0]$
5.1
\( 5 \)
\( 5^{8} \)
$15.32307$
$(a^3-2a^2-5a+1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{3} \)
$0.564514249$
$154.0884428$
1.240620741
\( \frac{105329076}{390625} a^{3} - \frac{187575264}{390625} a^{2} - \frac{525009912}{390625} a + \frac{21361121}{390625} \)
\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( 2 a^{3} - 2 a^{2} - 6 a + 2\) , \( 12 a^{3} - 10 a^{2} - 76 a - 33\bigr] \) ${y}^2+\left(a^{3}-a^{2}-6a-1\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-2a^{2}-6a+2\right){x}+12a^{3}-10a^{2}-76a-33$
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Pari/GP
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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.
