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
9.1-a4
9.1-a
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{8} \)
$0.63815$
$(3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$31.97784377$
0.969470791
\( \frac{274625}{81} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -22 a - 33\) , \( 71 a + 111\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-22a-33\right){x}+71a+111$
81.1-c4
81.1-c
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{20} \)
$1.10531$
$(3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$6.828410025$
0.414033173
\( \frac{274625}{81} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 195 a - 500\) , \( 1442 a - 3694\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(195a-500\right){x}+1442a-3694$
144.4-c4
144.4-c
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.4
\( 2^{4} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{8} \)
$1.27630$
$(-a+2), (3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$12.79720171$
0.775944329
\( \frac{274625}{81} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( 53 a - 135\) , \( 221 a - 566\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(53a-135\right){x}+221a-566$
144.5-c4
144.5-c
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
144.5
\( 2^{4} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{8} \)
$1.27630$
$(-a-1), (3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$12.79720171$
0.775944329
\( \frac{274625}{81} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -53 a - 82\) , \( -221 a - 345\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-53a-82\right){x}-221a-345$
576.6-e4
576.6-e
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.6
\( 2^{6} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.80496$
$(-a-1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.978485520$
$7.242622550$
3.437603564
\( \frac{274625}{81} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 43 a - 117\) , \( 188 a - 485\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(43a-117\right){x}+188a-485$
576.6-n4
576.6-n
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.6
\( 2^{6} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.80496$
$(-a-1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$0.839158111$
$9.048988114$
1.841701975
\( \frac{274625}{81} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7 a - 13\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-7a-13\right){x}$
576.7-e4
576.7-e
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.80496$
$(-a+2), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.978485520$
$7.242622550$
3.437603564
\( \frac{274625}{81} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -45 a - 72\) , \( -189 a - 296\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-45a-72\right){x}-189a-296$
576.7-n4
576.7-n
$8$
$16$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.7
\( 2^{6} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.80496$
$(-a+2), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$0.839158111$
$9.048988114$
1.841701975
\( \frac{274625}{81} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 10 a - 25\) , \( -25 a + 61\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-25\right){x}-25a+61$
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Pari/GP
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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.