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
$2$
$2$
5.5.160801.1
$5$
$[5, 0]$
17.1
\( 17 \)
\( - 17^{2} \)
$47.56942$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1806.587343$
2.25260267
\( -\frac{6305013282}{289} a^{4} + \frac{111511521455}{289} a^{3} + \frac{312426461031}{289} a^{2} + \frac{105425593932}{289} a - \frac{35862663406}{289} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{4} - 5 a^{2} + 2\) , \( -2 a^{4} + 14 a^{3} + 4 a^{2} - 23 a - 4\) , \( 3 a^{4} + 23 a^{3} - 44 a^{2} - 3 a + 18\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{4}+14a^{3}+4a^{2}-23a-4\right){x}+3a^{4}+23a^{3}-44a^{2}-3a+18$
17.1-a2
17.1-a
$2$
$2$
5.5.160801.1
$5$
$[5, 0]$
17.1
\( 17 \)
\( 17 \)
$47.56942$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$3613.174686$
2.25260267
\( -\frac{45163}{17} a^{4} + \frac{122611}{17} a^{3} - \frac{20123}{17} a^{2} - \frac{866560}{17} a + \frac{113007}{17} \)
\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{4} - 5 a^{2} + 2\) , \( 3 a^{4} + 4 a^{3} - 6 a^{2} - 8 a + 1\) , \( 6 a^{4} + 6 a^{3} - 18 a^{2} - a + 1\bigr] \)
${y}^2+\left(2a^{4}-a^{3}-9a^{2}+5a+2\right){x}{y}+\left(a^{4}-5a^{2}+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(3a^{4}+4a^{3}-6a^{2}-8a+1\right){x}+6a^{4}+6a^{3}-18a^{2}-a+1$
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Pari/GP
SageMath
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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.