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
$1$
$1$
4.4.5744.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( - 17^{3} \)
$9.65055$
$(a^2-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Ns
$1$
\( 1 \)
$1$
$184.4286477$
2.433442935
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \)
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -2 a^{3} + a^{2} + 8 a + 1\) , \( -a^{3} + a^{2} + 5 a\) , \( -3 a^{3} + a^{2} + 9 a\) , \( -11 a^{3} + 7 a^{2} + 45 a - 13\bigr] \)
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+8a+1\right){x}^{2}+\left(-3a^{3}+a^{2}+9a\right){x}-11a^{3}+7a^{2}+45a-13$
17.1-f1
17.1-f
$1$
$1$
4.4.5744.1
$4$
$[4, 0]$
17.1
\( 17 \)
\( - 17^{3} \)
$9.65055$
$(a^2-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Ns
$1$
\( 3 \)
$0.013859577$
$507.6259882$
1.113955591
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \)
\( \bigl[a^{2} - 2\) , \( -a^{3} + 6 a\) , \( a^{3} - 5 a\) , \( 8 a^{3} - 12 a^{2} - 21 a + 1\) , \( -22 a^{3} + 47 a^{2} + 23 a - 23\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(8a^{3}-12a^{2}-21a+1\right){x}-22a^{3}+47a^{2}+23a-23$
289.1-a1
289.1-a
$1$
$1$
4.4.5744.1
$4$
$[4, 0]$
289.1
\( 17^{2} \)
\( - 17^{9} \)
$13.75175$
$(a^2-2)$
$0 \le r \le 2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3Ns
$16$
\( 2^{2} \)
$1$
$3.842899832$
3.245127933
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \)
\( \bigl[a\) , \( a^{3} - a^{2} - 5 a\) , \( a\) , \( 22 a^{3} - 41 a^{2} - 29 a + 3\) , \( 94 a^{3} - 224 a^{2} - 5 a + 12\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(22a^{3}-41a^{2}-29a+3\right){x}+94a^{3}-224a^{2}-5a+12$
289.1-f1
289.1-f
$1$
$1$
4.4.5744.1
$4$
$[4, 0]$
289.1
\( 17^{2} \)
\( - 17^{9} \)
$13.75175$
$(a^2-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3Ns
$1$
\( 2 \)
$1$
$48.65022612$
1.283830364
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \)
\( \bigl[a^{3} - 5 a\) , \( a^{3} - a^{2} - 5 a\) , \( 0\) , \( -3 a^{3} - 12 a^{2} - 9 a\) , \( -7 a^{3} + 87 a^{2} + 169 a - 52\bigr] \)
${y}^2+\left(a^{3}-5a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-3a^{3}-12a^{2}-9a\right){x}-7a^{3}+87a^{2}+169a-52$
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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.