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
17.2-a1
17.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( 17 \)
$0.65422$
$(a-5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$22.24460707$
0.685504883
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-a-1\right){x}$
153.3-b1
153.3-b
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17 \)
$1.13314$
$(-a), (a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 1 \)
$1$
$5.249776806$
1.456026112
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2 a - 3\) , \( 3 a - 10\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2a-3\right){x}+3a-10$
153.5-b1
153.5-b
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
153.5
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17 \)
$1.13314$
$(-a+1), (a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.038584833$
$29.15019498$
1.247804091
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -2 a - 1\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}+a+1$
289.2-a1
289.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
289.2
\( 17^{2} \)
\( 17^{7} \)
$1.32842$
$(a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$5.005579451$
2.776595903
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -6 a - 9\) , \( -30 a - 38\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-9\right){x}-30a-38$
1377.2-k1
1377.2-k
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1377.2
\( 3^{4} \cdot 17 \)
\( 3^{12} \cdot 17 \)
$1.96265$
$(-a), (-a+1), (a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \)
$0.479666195$
$6.879510931$
3.660875779
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -9 a - 12\) , \( -30 a - 39\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-9a-12\right){x}-30a-39$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.