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
441.1-a1 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{2} \cdot 7^{16} \)
$0.81899$
$(3), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{3} \)
$0.746299208$
$0.862076929$
0.643367330
\( -\frac{4354703137}{17294403} \)
\( \bigl[i\) , \( 0\) , \( 0\) , \( -34\) , \( 217\bigr] \) ${y}^2+i{x}{y}={x}^{3}-34{x}+217$
441.1-a2 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{4} \cdot 7^{2} \)
$0.81899$
$(3), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2 \)
$0.373149604$
$6.896615437$
0.643367330
\( \frac{103823}{63} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
441.1-a3 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{8} \cdot 7^{4} \)
$0.81899$
$(3), (7)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{3} \)
$0.746299208$
$3.448307718$
0.643367330
\( \frac{7189057}{3969} \)
\( \bigl[i\) , \( 0\) , \( 0\) , \( -4\) , \( 1\bigr] \) ${y}^2+i{x}{y}={x}^{3}-4{x}+1$
441.1-a4 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{16} \cdot 7^{2} \)
$0.81899$
$(3), (7)$
$1$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2^{3} \)
$1.492598417$
$1.724153859$
0.643367330
\( \frac{6570725617}{45927} \)
\( \bigl[i\) , \( 0\) , \( 0\) , \( -39\) , \( -90\bigr] \) ${y}^2+i{x}{y}={x}^{3}-39{x}-90$
441.1-a5 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{4} \cdot 7^{8} \)
$0.81899$
$(3), (7)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{3} \)
$1.492598417$
$1.724153859$
0.643367330
\( \frac{13027640977}{21609} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
441.1-a6 441.1-a $6$
$8$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{2} \cdot 7^{4} \)
$0.81899$
$(3), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2B $1$
\( 2 \)
$2.985196834$
$0.862076929$
0.643367330
\( \frac{53297461115137}{147} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
