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
17.1-a1 17.1-a $4$
$4$
3.3.148.1 $3$
$[3, 0]$
17.1
\( 17 \)
\( 17 \)
$1.74319$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$27.09027313$
0.556701683
\( \frac{1166385842037470}{17} a^{2} - \frac{2894050974029619}{17} a + \frac{787508804920048}{17} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 238 a^{2} - 154 a - 789\) , \( -2388 a^{2} + 1668 a + 7624\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(238a^{2}-154a-789\right){x}-2388a^{2}+1668a+7624$
17.1-a2 17.1-a $4$
$4$
3.3.148.1 $3$
$[3, 0]$
17.1
\( 17 \)
\( - 17^{4} \)
$1.74319$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$6.772568284$
0.556701683
\( \frac{2039354031507687810}{83521} a^{2} + \frac{2386220594007153091}{83521} a - \frac{939757029887526432}{83521} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 28 a^{2} - 24 a - 99\) , \( 108 a^{2} - 86 a - 366\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(28a^{2}-24a-99\right){x}+108a^{2}-86a-366$
17.1-a3 17.1-a $4$
$4$
3.3.148.1 $3$
$[3, 0]$
17.1
\( 17 \)
\( 17^{2} \)
$1.74319$
$(2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2 \)
$1$
$54.18054627$
0.556701683
\( \frac{1479738789}{289} a^{2} - \frac{1677591684}{289} a + \frac{392777968}{289} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 13 a^{2} - 9 a - 44\) , \( -22 a^{2} + 15 a + 69\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(13a^{2}-9a-44\right){x}-22a^{2}+15a+69$
17.1-a4 17.1-a $4$
$4$
3.3.148.1 $3$
$[3, 0]$
17.1
\( 17 \)
\( 17 \)
$1.74319$
$(2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$108.3610925$
0.556701683
\( \frac{6748}{17} a^{2} - \frac{43238}{17} a + \frac{12799}{17} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( -2 a^{2} + a + 6\) , \( -3 a^{2} + 2 a + 9\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{2}+a+6\right){x}-3a^{2}+2a+9$
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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.
