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
1.1-a1
1.1-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.2 , 5B
$9$
\( 1 \)
$1$
$4.286906993$
2.549581091
\( -299510191348095 a + 2415960913292737 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 22 a - 285\) , \( 307 a - 3606\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(22a-285\right){x}+307a-3606$
1.1-a2
1.1-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.1 , 5B
$9$
\( 1 \)
$1$
$38.58216293$
2.549581091
\( -888615 a + 7334137 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 3\) , \( 2 a + 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(a-3\right){x}+2a+6$
1.1-a3
1.1-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.1 , 5B
$9$
\( 1 \)
$1$
$38.58216293$
2.549581091
\( 888615 a + 6445522 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -3 a\) , \( -3 a + 9\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-3a{x}-3a+9$
1.1-a4
1.1-a
$4$
$15$
\(\Q(\sqrt{229}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.2 , 5B
$9$
\( 1 \)
$1$
$4.286906993$
2.549581091
\( 299510191348095 a + 2116450721944642 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -24 a - 263\) , \( -308 a - 3299\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-24a-263\right){x}-308a-3299$
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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.