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
5202.1-a1
5202.1-a
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.1
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2^{6} \cdot 3^{7} \cdot 17^{2} \)
$2.14648$
$(a), (-a-1), (-2a+3)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{3} \)
$0.035586375$
$3.063864834$
2.467109039
\( -\frac{3575}{24} a + \frac{96797}{24} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -4 a - 5\) , \( 3 a - 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-5\right){x}+3a-1$
5202.1-a2
5202.1-a
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.1
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2^{2} \cdot 3^{9} \cdot 17^{2} \)
$2.14648$
$(a), (-a-1), (-2a+3)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{3} \)
$0.035586375$
$3.063864834$
2.467109039
\( \frac{243529}{54} a + \frac{352727}{54} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 2 a - 7\) , \( 2 a - 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(2a-7\right){x}+2a-6$
5202.1-b1
5202.1-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.1
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2^{6} \cdot 3^{7} \cdot 17^{8} \)
$2.14648$
$(a), (-a-1), (-2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$0.743096372$
2.101793936
\( -\frac{3575}{24} a + \frac{96797}{24} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 55 a - 68\) , \( -228 a + 72\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(55a-68\right){x}-228a+72$
5202.1-b2
5202.1-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.1
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2^{2} \cdot 3^{9} \cdot 17^{8} \)
$2.14648$
$(a), (-a-1), (-2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2^{2} \)
$1$
$0.743096372$
2.101793936
\( \frac{243529}{54} a + \frac{352727}{54} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 78 a + 55\) , \( 73 a + 569\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(78a+55\right){x}+73a+569$
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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.