| 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 |
| 225.7-CMa1 |
225.7-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$2.977452843$ |
1.795471620 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -5 a + 8\) , \( -a + 9\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+8\right){x}-a+9$ |
| 225.7-a1 |
225.7-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{11} \cdot 5^{8} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.395636541$ |
$0.692871952$ |
1.554990352 |
\( \frac{10449954757}{243} a - \frac{3680765176}{81} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 329 a - 22\) , \( 1370 a + 3718\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(329a-22\right){x}+1370a+3718$ |
| 225.7-a2 |
225.7-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{21} \cdot 5^{8} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$0.465212180$ |
$0.692871952$ |
1.554990352 |
\( \frac{507968593}{14348907} a + \frac{3353625341}{4782969} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 26 a + 48\) , \( 127 a + 116\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(26a+48\right){x}+127a+116$ |
| 225.7-a3 |
225.7-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{9} \cdot 5^{4} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 2^{2} \) |
$0.093042436$ |
$3.464359763$ |
1.554990352 |
\( -\frac{24167}{27} a + \frac{17576}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( a - 2\) , \( -2 a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-2\right){x}-2a+2$ |
| 225.7-a4 |
225.7-a |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{7} \cdot 5^{4} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.279127308$ |
$3.464359763$ |
1.554990352 |
\( -\frac{77363}{3} a + 34089 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 3\) , \( 4 a - 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+3\right){x}+4a-13$ |
| 225.7-b1 |
225.7-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{11} \cdot 5^{2} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.549308785$ |
1.868536700 |
\( \frac{10449954757}{243} a - \frac{3680765176}{81} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -24 a + 116\) , \( -273 a - 128\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-24a+116\right){x}-273a-128$ |
| 225.7-b2 |
225.7-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{21} \cdot 5^{2} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.549308785$ |
1.868536700 |
\( \frac{507968593}{14348907} a + \frac{3353625341}{4782969} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -7 a + 10\) , \( -15 a + 17\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+10\right){x}-15a+17$ |
| 225.7-b3 |
225.7-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{9} \cdot 5^{10} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.549308785$ |
1.868536700 |
\( -\frac{24167}{27} a + \frac{17576}{9} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -9 a - 11\) , \( 17 a + 8\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-9a-11\right){x}+17a+8$ |
| 225.7-b4 |
225.7-b |
$4$ |
$15$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
225.7 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{7} \cdot 5^{10} \) |
$1.14784$ |
$(a-1), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B |
$1$ |
\( 2 \) |
$1$ |
$1.549308785$ |
1.868536700 |
\( -\frac{77363}{3} a + 34089 \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 13 a - 40\) , \( -44 a + 94\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(13a-40\right){x}-44a+94$ |
*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.
