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
$4$
$6$
4.4.14272.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( 17^{2} \)
$15.21203$
$(a^3-3a^2-2a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$9$
\( 2 \)
$1$
$94.42352016$
3.556724957
\( \frac{13834806373280509636740011174}{289} a^{3} - \frac{37580309182394739748115559673}{289} a^{2} - \frac{42253016405658218695644998246}{289} a + \frac{57937966910413693362695212289}{289} \)
\( \bigl[a\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 436 a^{3} - 541 a^{2} - 2889 a - 1731\) , \( -12800 a^{3} + 12436 a^{2} + 73729 a + 42292\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(436a^{3}-541a^{2}-2889a-1731\right){x}-12800a^{3}+12436a^{2}+73729a+42292$
17.1-b1
17.1-b
$4$
$6$
4.4.14272.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( 17^{2} \)
$15.21203$
$(a^3-3a^2-2a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$9$
\( 2 \)
$3.490744549$
$4.207340861$
2.212869756
\( \frac{13834806373280509636740011174}{289} a^{3} - \frac{37580309182394739748115559673}{289} a^{2} - \frac{42253016405658218695644998246}{289} a + \frac{57937966910413693362695212289}{289} \)
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -848 a^{3} + 2260 a^{2} + 2564 a - 3510\) , \( -22808 a^{3} + 61558 a^{2} + 69436 a - 95032\bigr] \)
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(-848a^{3}+2260a^{2}+2564a-3510\right){x}-22808a^{3}+61558a^{2}+69436a-95032$
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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.