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
153.5-a1
153.5-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
153.5
\( 3^{2} \cdot 17 \)
\( 3^{8} \cdot 17^{3} \)
$1.13314$
$(-a+1), (a-5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$9.417264342$
1.741252792
\( -\frac{78540800}{44217} a - \frac{21905408}{14739} \)
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -3 a + 3\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+3\right){x}+a+1$
153.5-a2
153.5-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
153.5
\( 3^{2} \cdot 17 \)
\( 3^{12} \cdot 17 \)
$1.13314$
$(-a+1), (a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \)
$1$
$3.139088114$
1.741252792
\( \frac{439988224}{12393} a - \frac{331145216}{4131} \)
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 4 a + 2\) , \( -a - 9\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+2\right){x}-a-9$
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
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -2 a - 1\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}+a+1$
153.5-b2
153.5-b
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
153.5
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.13314$
$(-a+1), (a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.115754499$
$9.716731661$
1.247804091
\( \frac{2659135311872}{4913} a - \frac{6123387461632}{4913} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 18 a + 9\) , \( -40 a - 15\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(18a+9\right){x}-40a-15$
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.