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
8.3-a1 8.3-a $2$
$3$
4.4.17428.1 $4$
$[4, 0]$
8.3
\( 2^{3} \)
\( 2^{11} \)
$15.29849$
$(a^3+a^2-3a-2), (-a^2+2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B $1$
\( 1 \)
$0.163226853$
$648.2468780$
3.206034989
\( -\frac{1971}{2} a^{3} + \frac{1517}{2} a^{2} + \frac{8813}{2} a - \frac{7247}{2} \)
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -7 a^{3} - 7 a^{2} + 25 a + 20\) , \( 6 a^{3} + 10 a^{2} - 11 a - 12\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-7a^{3}-7a^{2}+25a+20\right){x}+6a^{3}+10a^{2}-11a-12$
8.3-a2 8.3-a $2$
$3$
4.4.17428.1 $4$
$[4, 0]$
8.3
\( 2^{3} \)
\( 2^{17} \)
$15.29849$
$(a^3+a^2-3a-2), (-a^2+2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B $1$
\( 3 \)
$0.054408951$
$648.2468780$
3.206034989
\( -\frac{6623193813}{4} a^{3} - \frac{9064833529}{4} a^{2} + \frac{36535505751}{8} a + \frac{33554288521}{8} \)
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -a^{3} - 5 a^{2} + 5 a + 25\) , \( -3 a^{2} + 14\bigr] \) ${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{3}-5a^{2}+5a+25\right){x}-3a^{2}+14$
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Pari/GP
SageMath
Magma
Oscar
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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.
