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
1083.2-b3 1083.2-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
1083.2
\( 3 \cdot 19^{2} \)
\( 3^{2} \cdot 19^{8} \)
$0.88788$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{3} \)
$1$
$1.632344499$
0.942434535
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$
61731.2-b2 61731.2-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
61731.2
\( 3^{2} \cdot 19^{3} \)
\( 3^{8} \cdot 19^{14} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{6} \)
$1$
$0.216209310$
0.998628029
\( \frac{67419143}{390963} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 407 a - 535\) , \( 4786 a + 8982\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(407a-535\right){x}+4786a+8982$
61731.3-b2 61731.3-b $6$
$8$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
61731.3
\( 3^{2} \cdot 19^{3} \)
\( 3^{8} \cdot 19^{14} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{6} \)
$1$
$0.216209310$
0.998628029
\( \frac{67419143}{390963} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -128 a + 535\) , \( -4787 a + 13769\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-128a+535\right){x}-4787a+13769$
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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.
