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
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{16} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.680639832$
0.815230064
\( -\frac{150435795683}{4374} a + \frac{1155932622647}{13122} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 304 a - 779\) , \( 4017 a - 10293\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(304a-779\right){x}+4017a-10293$
18.1-a2
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2^{2} \cdot 3^{2} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$26.89023731$
0.815230064
\( -\frac{59090945}{12} a + \frac{151366337}{12} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( a + 1\) , \( -2 a - 3\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}-2a-3$
18.1-a3
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2^{8} \cdot 3^{2} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$26.89023731$
0.815230064
\( \frac{1095125}{768} a + \frac{2055079}{768} \)
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}+1$
18.1-a4
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$26.89023731$
0.815230064
\( \frac{173375}{144} a + \frac{1033157}{144} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 4 a - 9\) , \( -7 a + 17\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(4a-9\right){x}-7a+17$
18.1-a5
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( 2^{2} \cdot 3^{8} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$6.722559329$
0.815230064
\( \frac{2360605505}{108} a + \frac{11062735109}{324} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 19 a - 49\) , \( 53 a - 139\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(19a-49\right){x}+53a-139$
18.1-a6
18.1-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.1
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{4} \)
$0.75889$
$(-a+2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$1.680639832$
0.815230064
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \)
\( \bigl[1\) , \( a\) , \( a\) , \( -26 a + 41\) , \( 269 a - 769\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-26a+41\right){x}+269a-769$
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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.