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
1444.1-a1
1444.1-a
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1444.1
\( 2^{2} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.55803$
$(a), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$0.090182329$
$12.37307863$
2.367039347
\( \frac{178204879872}{19} a - \frac{252019758080}{19} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( a - 6\) , \( -32 a - 40\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(a-6\right){x}-32a-40$
1444.1-b1
1444.1-b
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1444.1
\( 2^{2} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.55803$
$(a), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$0.090182329$
$12.37307863$
2.367039347
\( -\frac{178204879872}{19} a - \frac{252019758080}{19} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -a - 6\) , \( 32 a - 40\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-a-6\right){x}+32a-40$
1444.1-c1
1444.1-c
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1444.1
\( 2^{2} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.55803$
$(a), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$0.056475061$
$19.78350515$
2.370097498
\( -\frac{3740000}{19} a - \frac{5277168}{19} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 2\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+2\right){x}$
1444.1-d1
1444.1-d
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1444.1
\( 2^{2} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.55803$
$(a), (19)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$2.466064026$
0.871885298
\( -\frac{4194304}{19} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -5\) , \( -7\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}-5{x}-7$
1444.1-e1
1444.1-e
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1444.1
\( 2^{2} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.55803$
$(a), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 3 \)
$0.056475061$
$19.78350515$
2.370097498
\( \frac{3740000}{19} a - \frac{5277168}{19} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 2\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+2\right){x}$
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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.