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 $2$
$2$
4.4.19821.1 $4$
$[4, 0]$
17.1
\( 17 \)
\( 17 \)
$17.92699$
$(a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$1473.805653$
2.617082696
\( -\frac{30069856}{51} a^{3} - \frac{57403081}{51} a^{2} + \frac{24388892}{17} a + \frac{10411556}{17} \)
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( 2 a^{3} - 17 a + 4\) , \( \frac{7}{3} a^{3} + \frac{1}{3} a^{2} - 20 a - 1\bigr] \) ${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-4a+1\right){x}^{2}+\left(2a^{3}-17a+4\right){x}+\frac{7}{3}a^{3}+\frac{1}{3}a^{2}-20a-1$
17.1-a2 17.1-a $2$
$2$
4.4.19821.1 $4$
$[4, 0]$
17.1
\( 17 \)
\( - 17^{2} \)
$17.92699$
$(a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$736.9028267$
2.617082696
\( \frac{9878307305244158}{867} a^{3} + \frac{18933234918159542}{867} a^{2} - \frac{7934960729500279}{289} a - \frac{3386870152613548}{289} \)
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - 2 a + 9\) , \( \frac{19}{3} a^{3} - \frac{2}{3} a^{2} - 48 a - 11\bigr] \) ${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-4a+1\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-2a+9\right){x}+\frac{19}{3}a^{3}-\frac{2}{3}a^{2}-48a-11$
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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.
