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
1.1-a1
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2 a + 10\) , \( 2 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a+10\right){x}+2a+7$
1.1-a2
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4 a + 3\) , \( a + 21\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(4a+3\right){x}+a+21$
1.1-a3
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( 16581375 \)
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -18 a - 65\) , \( 41 a + 153\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-18a-65\right){x}+41a+153$
1.1-a4
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( 16581375 \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 24 a - 72\) , \( -113 a + 447\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(24a-72\right){x}-113a+447$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.