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-a4
18.2-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( 2^{2} \cdot 3^{8} \)
$0.75889$
$(-a-1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$6.722559329$
0.815230064
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -20 a - 30\) , \( -54 a - 86\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-30\right){x}-54a-86$
144.5-d4
144.5-d
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.5
\( 2^{4} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{8} \)
$1.27630$
$(-a-1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1.835336495$
$5.020615261$
2.234848983
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -41 a - 75\) , \( 136 a + 200\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-41a-75\right){x}+136a+200$
162.2-a4
162.2-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
162.2
\( 2 \cdot 3^{4} \)
\( 2^{2} \cdot 3^{20} \)
$1.31444$
$(-a-1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$9.757425008$
1.183261586
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -171 a - 282\) , \( 1714 a + 2703\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-171a-282\right){x}+1714a+2703$
288.4-c4
288.4-c
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
288.4
\( 2^{5} \cdot 3^{2} \)
\( 2^{14} \cdot 3^{8} \)
$1.51779$
$(-a+2), (-a-1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$0.370056505$
$9.798829194$
1.758926798
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -126 a - 200\) , \( -1156 a - 1804\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-126a-200\right){x}-1156a-1804$
576.6-h4
576.6-h
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.6
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{8} \)
$1.80496$
$(-a-1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$6.928818571$
1.680485342
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 48 a - 153\) , \( -405 a + 900\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(48a-153\right){x}-405a+900$
576.6-k4
576.6-k
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.6
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{8} \)
$1.80496$
$(-a-1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$10.34931208$
1.255038437
\( -\frac{2360605505}{108} a + \frac{4536137906}{81} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -601 a - 942\) , \( 10760 a + 16804\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-601a-942\right){x}+10760a+16804$
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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.