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
18.1-a1
18.1-a
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$1.37737$
$(-a+4), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.501880177$
1.136111527
\( \frac{4913}{1296} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2\) , \( -38 a - 142\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+2{x}-38a-142$
18.1-a2
18.1-a
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{4} \cdot 3^{16} \)
$1.37737$
$(-a+4), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.501880177$
1.136111527
\( \frac{838561807}{26244} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -80 a - 298\) , \( -738 a - 2762\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-80a-298\right){x}-738a-2762$
18.1-b1
18.1-b
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$1.37737$
$(-a+4), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.501880177$
1.136111527
\( \frac{4913}{1296} \)
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -a + 2\) , \( 38 a - 142\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+2\right){x}+38a-142$
18.1-b2
18.1-b
$2$
$2$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{4} \cdot 3^{16} \)
$1.37737$
$(-a+4), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.501880177$
1.136111527
\( \frac{838561807}{26244} \)
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 79 a - 298\) , \( 738 a - 2762\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(79a-298\right){x}+738a-2762$
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.