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
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( -19 \)
$2.20745$
$(a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$4.134983576$
$10.05169650$
7.025530673
\( \frac{1866240}{19} a - \frac{10977984}{19} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( -9 a - 62\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}-9a-62$
19.1-b1
19.1-b
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 2^{12} \cdot 19 \)
$2.20745$
$(a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.4
$1$
\( 1 \)
$1$
$55.57807397$
4.697204568
\( \frac{1866240}{19} a - \frac{10977984}{19} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 13\) , \( -4 a + 24\bigr] \)
${y}^2={x}^{3}+\left(2a-13\right){x}-4a+24$
19.1-c1
19.1-c
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( -19 \)
$2.20745$
$(a+4)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$55.57807397$
0.187888182
\( \frac{1866240}{19} a - \frac{10977984}{19} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( 3 a + 9\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$
19.1-d1
19.1-d
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 2^{12} \cdot 19 \)
$2.20745$
$(a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$0.969321370$
$10.05169650$
1.646922386
\( \frac{1866240}{19} a - \frac{10977984}{19} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 13\) , \( 4 a - 24\bigr] \)
${y}^2={x}^{3}+\left(2a-13\right){x}+4a-24$
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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.