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
23104.1-a1
23104.1-a
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
23104.1
\( 2^{6} \cdot 19^{2} \)
\( 2^{12} \cdot 19^{2} \)
$2.20338$
$(a+1), (19)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$0.058229357$
$4.183446943$
3.897590849
\( -\frac{13824}{19} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -2 i\bigr] \)
${y}^2={x}^{3}+2{x}-2i$
23104.1-b1
23104.1-b
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
23104.1
\( 2^{6} \cdot 19^{2} \)
\( 2^{6} \cdot 19^{2} \)
$2.20338$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$0.314996586$
$5.963775842$
3.757138071
\( \frac{27000}{19} \)
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -2\) , \( -i\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-2{x}-i$
23104.1-c1
23104.1-c
$3$
$25$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
23104.1
\( 2^{6} \cdot 19^{2} \)
\( 2^{12} \cdot 19^{2} \)
$2.20338$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B
$1$
\( 2 \)
$1.806491839$
$0.603483608$
4.360752859
\( -\frac{5698354821120}{19} a - \frac{4288599378432}{19} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1080 i - 1186\) , \( 22126 i - 11040\bigr] \)
${y}^2={x}^{3}+\left(1080i-1186\right){x}+22126i-11040$
23104.1-c2
23104.1-c
$3$
$25$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
23104.1
\( 2^{6} \cdot 19^{2} \)
\( 2^{12} \cdot 19^{2} \)
$2.20338$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B
$1$
\( 2 \)
$1.806491839$
$0.603483608$
4.360752859
\( \frac{5698354821120}{19} a - \frac{4288599378432}{19} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1080 i - 1186\) , \( -22126 i - 11040\bigr] \)
${y}^2={x}^{3}+\left(-1080i-1186\right){x}-22126i-11040$
23104.1-c3
23104.1-c
$3$
$25$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
23104.1
\( 2^{6} \cdot 19^{2} \)
\( 2^{12} \cdot 19^{10} \)
$2.20338$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5Cs
$1$
\( 2 \cdot 5 \)
$0.361298367$
$0.603483608$
4.360752859
\( -\frac{4741632}{2476099} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 14\) , \( 606 i\bigr] \)
${y}^2={x}^{3}+14{x}+606i$
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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.