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-a2
19.1-a
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 19^{5} \)
$2.20745$
$(a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 5 \)
$0.826996715$
$10.05169650$
7.025530673
\( \frac{19429567370408448}{2476099} a + \frac{114946874211721536}{2476099} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -825 a - 4895\) , \( 26910 a + 159193\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-825a-4895\right){x}+26910a+159193$
19.1-b2
19.1-b
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 2^{12} \cdot 19^{5} \)
$2.20745$
$(a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.3
$25$
\( 1 \)
$1$
$2.223122958$
4.697204568
\( \frac{19429567370408448}{2476099} a + \frac{114946874211721536}{2476099} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -38 a - 53\) , \( -116 a - 1096\bigr] \)
${y}^2={x}^{3}+\left(-38a-53\right){x}-116a-1096$
19.1-c2
19.1-c
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 19^{5} \)
$2.20745$
$(a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 1 \)
$1$
$2.223122958$
0.187888182
\( \frac{19429567370408448}{2476099} a + \frac{114946874211721536}{2476099} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -825 a - 4895\) , \( -36806 a - 217756\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-825a-4895\right){x}-36806a-217756$
19.1-d2
19.1-d
$2$
$5$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
19.1
\( 19 \)
\( - 2^{12} \cdot 19^{5} \)
$2.20745$
$(a+4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 5 \)
$0.193864274$
$10.05169650$
1.646922386
\( \frac{19429567370408448}{2476099} a + \frac{114946874211721536}{2476099} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -38 a - 53\) , \( 116 a + 1096\bigr] \)
${y}^2={x}^{3}+\left(-38a-53\right){x}+116a+1096$
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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.