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-a8
18.1-a
$8$
$20$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2^{5} \cdot 3^{22} \)
$2.14648$
$(-a-6), (3,a+1), (3,a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B
$16$
\( 2^{2} \cdot 5 \)
$1$
$0.435939855$
2.990522735
\( \frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -55482437 a - 323515405\) , \( -543123237520 a - 3166925470939\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-55482437a-323515405\right){x}-543123237520a-3166925470939$
18.1-f8
18.1-f
$8$
$20$
\(\Q(\sqrt{34}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2^{5} \cdot 3^{22} \)
$2.14648$
$(-a-6), (3,a+1), (3,a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B
$4$
\( 2^{4} \cdot 5 \)
$1$
$0.435939855$
2.990522735
\( \frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11307 a - 66186\) , \( -1602674 a - 9348007\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11307a-66186\right){x}-1602674a-9348007$
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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.