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
19.1-a1 19.1-a $1$
$1$
4.4.5125.1 $4$
$[4, 0]$
19.1
\( 19 \)
\( 19^{2} \)
$9.24336$
$(a^3-2a^2-3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$1$
$57.02749930$
1.593189328
\( -\frac{97722368}{361} a^{3} - \frac{69640192}{361} a^{2} + \frac{21032960}{19} a + \frac{398553088}{361} \)
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 8\) , \( -a^{3} + 3 a^{2} + 3 a - 11\bigr] \) ${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(a^{3}-2a^{2}-4a+8\right){x}-a^{3}+3a^{2}+3a-11$
19.1-b1 19.1-b $1$
$1$
4.4.5125.1 $4$
$[4, 0]$
19.1
\( 19 \)
\( 19^{2} \)
$9.24336$
$(a^3-2a^2-3a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$0.008997105$
$2008.533719$
2.019412344
\( -\frac{97722368}{361} a^{3} - \frac{69640192}{361} a^{2} + \frac{21032960}{19} a + \frac{398553088}{361} \)
\( \bigl[0\) , \( -a^{3} + 6 a + 4\) , \( a^{2} - 3\) , \( -7 a^{3} - 4 a^{2} + 32 a + 32\) , \( 11 a^{3} + 9 a^{2} - 43 a - 45\bigr] \) ${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(-7a^{3}-4a^{2}+32a+32\right){x}+11a^{3}+9a^{2}-43a-45$
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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.
