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
1225.2-a3
1225.2-a
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{6} \)
$1.75335$
$(-a-1), (a-2), (7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$1$
$2.324925606$
0.467327630
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+9{x}+1$
6125.2-d3
6125.2-d
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6125.2
\( 5^{3} \cdot 7^{2} \)
\( 5^{12} \cdot 7^{6} \)
$2.62187$
$(-a-1), (a-2), (7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$1$
$1.039738339$
3.761914858
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 27 a - 18\) , \( 5 a - 14\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a-18\right){x}+5a-14$
6125.3-c3
6125.3-c
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6125.3
\( 5^{3} \cdot 7^{2} \)
\( 5^{12} \cdot 7^{6} \)
$2.62187$
$(-a-1), (a-2), (7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$1$
$1.039738339$
3.761914858
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -25 a + 8\) , \( 21 a - 17\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-25a+8\right){x}+21a-17$
30625.3-c3
30625.3-c
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
30625.3
\( 5^{4} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{6} \)
$3.92061$
$(-a-1), (a-2), (7)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2^{4} \cdot 3 \)
$0.069271959$
$0.464985121$
3.729335107
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 217\) , \( -282\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+217{x}-282$
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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.