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
20449.1-a1 20449.1-a $3$
$25$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
20449.1
\( 11^{2} \cdot 13^{2} \)
\( 11^{2} \cdot 13^{6} \)
$1.85083$
$(-4a+1), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.4.2 $1$
\( 2 \)
$6.923571309$
$0.102705161$
3.284367889
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -62563 a + 117305\) , \( -9543612 a - 4543418\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-62563a+117305\right){x}-9543612a-4543418$
20449.1-a2 20449.1-a $3$
$25$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
20449.1
\( 11^{2} \cdot 13^{2} \)
\( 11^{10} \cdot 13^{6} \)
$1.85083$
$(-4a+1), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5Cs.4.1 $1$
\( 2 \)
$1.384714261$
$0.513525805$
3.284367889
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -83 a + 155\) , \( -782 a - 418\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-83a+155\right){x}-782a-418$
20449.1-a3 20449.1-a $3$
$25$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
20449.1
\( 11^{2} \cdot 13^{2} \)
\( 11^{2} \cdot 13^{6} \)
$1.85083$
$(-4a+1), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.4.1 $1$
\( 2 \)
$0.276942852$
$2.567629028$
3.284367889
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3 a + 5\) , \( 8 a + 2\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+5\right){x}+8a+2$
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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.
