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
1886.1-a1
1886.1-a
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1886.1
\( 2 \cdot 23 \cdot 41 \)
\( 2 \cdot 23^{2} \cdot 41 \)
$1.66559$
$(a), (-a-5), (-2a+7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$3.978994940$
2.813574304
\( \frac{1749839883}{43378} a - \frac{1237316965}{21689} \)
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 0\) , \( -6 a - 9\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-6a-9$
1886.1-b1
1886.1-b
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1886.1
\( 2 \cdot 23 \cdot 41 \)
\( 2^{7} \cdot 23^{2} \cdot 41^{3} \)
$1.66559$
$(a), (-a-5), (-2a+7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \cdot 3 \cdot 7 \)
$0.031392961$
$3.736226728$
3.483371531
\( -\frac{70746971251}{583347344} a - \frac{43912058253}{291673672} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -8 a - 9\) , \( -29 a - 39\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-8a-9\right){x}-29a-39$
1886.1-c1
1886.1-c
$1$
$1$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1886.1
\( 2 \cdot 23 \cdot 41 \)
\( 2^{16} \cdot 23 \cdot 41 \)
$1.66559$
$(a), (-a-5), (-2a+7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.361452638$
$3.294478704$
1.684042709
\( -\frac{4093673079}{241408} a - \frac{5524441249}{241408} \)
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -10 a + 12\) , \( -18 a + 22\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-10a+12\right){x}-18a+22$
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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.