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 $4$
$4$
5.5.24217.1 $5$
$[5, 0]$
17.1
\( 17 \)
\( 17 \)
$18.46051$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$477.4099648$
0.766957533
\( -\frac{1244011801477449574}{17} a^{4} + \frac{918347035277191526}{17} a^{3} + \frac{5597927007057751004}{17} a^{2} - \frac{2807449966148629537}{17} a - \frac{1733261045969695639}{17} \)
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 7 a - 3\) , \( 1\) , \( 21 a^{4} + 14 a^{3} - 92 a^{2} - 79 a - 22\) , \( 74 a^{4} + 7 a^{3} - 324 a^{2} - 87 a + 12\bigr] \) ${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+{y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-7a-3\right){x}^{2}+\left(21a^{4}+14a^{3}-92a^{2}-79a-22\right){x}+74a^{4}+7a^{3}-324a^{2}-87a+12$
17.1-a2 17.1-a $4$
$4$
5.5.24217.1 $5$
$[5, 0]$
17.1
\( 17 \)
\( 17^{2} \)
$18.46051$
$(a^2-a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2 \)
$1$
$954.8199297$
0.766957533
\( -\frac{54226785940}{289} a^{4} + \frac{41617197320}{289} a^{3} + \frac{246699945345}{289} a^{2} - \frac{124059587666}{289} a - \frac{76459531031}{289} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 6 a + 7\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -28 a^{4} + 14 a^{3} + 124 a^{2} - 21 a - 65\) , \( -92 a^{4} + 50 a^{3} + 410 a^{2} - 78 a - 227\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+6a+7\right){x}^{2}+\left(-28a^{4}+14a^{3}+124a^{2}-21a-65\right){x}-92a^{4}+50a^{3}+410a^{2}-78a-227$
17.1-a3 17.1-a $4$
$4$
5.5.24217.1 $5$
$[5, 0]$
17.1
\( 17 \)
\( 17 \)
$18.46051$
$(a^2-a-3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$1909.639859$
0.766957533
\( -\frac{171999}{17} a^{4} + \frac{116660}{17} a^{3} + \frac{748638}{17} a^{2} - \frac{385756}{17} a - \frac{232095}{17} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 3 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 2 a^{4} - 9 a^{2} + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} + 12 a + 9\) , \( 5 a^{4} - 2 a^{3} - 23 a^{2} + 4 a + 5\bigr] \) ${y}^2+\left(2a^{4}-a^{3}-9a^{2}+3a+4\right){x}{y}+\left(2a^{4}-9a^{2}+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(5a^{4}-4a^{3}-23a^{2}+12a+9\right){x}+5a^{4}-2a^{3}-23a^{2}+4a+5$
17.1-a4 17.1-a $4$
$4$
5.5.24217.1 $5$
$[5, 0]$
17.1
\( 17 \)
\( - 17^{4} \)
$18.46051$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $4$
\( 2^{2} \)
$1$
$29.83812280$
0.766957533
\( -\frac{53619990153098106}{83521} a^{4} - \frac{118313872970940038}{83521} a^{3} + \frac{303817425868498660}{83521} a^{2} + \frac{402918681349569873}{83521} a + \frac{102459100667346615}{83521} \)
\( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( -a^{2} - a + 1\) , \( 0\) , \( -115 a^{4} + 41 a^{3} + 555 a^{2} - 83 a - 318\) , \( -757 a^{4} + 282 a^{3} + 3694 a^{2} - 572 a - 2090\bigr] \) ${y}^2+\left(3a^{4}-a^{3}-14a^{2}+3a+5\right){x}{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-115a^{4}+41a^{3}+555a^{2}-83a-318\right){x}-757a^{4}+282a^{3}+3694a^{2}-572a-2090$
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Pari/GP
SageMath
Magma
Oscar
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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.
