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
18.2-a1
18.2-a
$2$
$2$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( 2^{2} \cdot 3^{8} \)
$2.14648$
$(-a-6), (3,a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.453500819$
$27.72261764$
2.156119626
\( \frac{44264}{9} a + \frac{547409}{18} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -10 a - 58\) , \( 12 a + 70\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-58\right){x}+12a+70$
18.2-a2
18.2-a
$2$
$2$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{10} \)
$2.14648$
$(-a-6), (3,a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.907001639$
$13.86130882$
2.156119626
\( \frac{47283569531}{162} a + \frac{137854249184}{81} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -305 a - 1778\) , \( 5419 a + 31598\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-305a-1778\right){x}+5419a+31598$
18.2-b1
18.2-b
$2$
$2$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( 2^{2} \cdot 3^{8} \)
$2.14648$
$(-a-6), (3,a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.555734509$
$27.72261764$
2.642178430
\( \frac{44264}{9} a + \frac{547409}{18} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 11 a - 64\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(11a-64\right){x}$
18.2-b2
18.2-b
$2$
$2$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{10} \)
$2.14648$
$(-a-6), (3,a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.111469019$
$13.86130882$
2.642178430
\( \frac{47283569531}{162} a + \frac{137854249184}{81} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -44 a + 256\) , \( 33 a - 192\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-44a+256\right){x}+33a-192$
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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.