| 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 |
| 18396.3-a1 |
18396.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{2} \cdot 3^{9} \cdot 7^{3} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.042854091$ |
$2.311303557$ |
2.744921258 |
\( \frac{184898138}{225351} a + \frac{97664167}{450702} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a - 6\) , \( 9 a + 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a-6\right){x}+9a+2$ |
| 18396.3-b1 |
18396.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{10} \cdot 3^{3} \cdot 7 \cdot 73 \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.036074370$ |
$3.488616021$ |
2.906372638 |
\( \frac{1916367}{16352} a + \frac{25136205}{16352} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 3 a + 1\) , \( 2 a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a+1\right){x}+2a-1$ |
| 18396.3-c1 |
18396.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{10} \cdot 3^{15} \cdot 7^{5} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.171788734$ |
$0.379140799$ |
3.008323687 |
\( \frac{12211771579546037}{9540459936} a - \frac{8276222324659201}{9540459936} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -1233 a + 309\) , \( 14433 a - 11979\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1233a+309\right){x}+14433a-11979$ |
| 18396.3-d1 |
18396.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{4} \cdot 73^{2} \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.418207293$ |
$1.573380882$ |
3.039168860 |
\( \frac{146913674955}{25589858} a - \frac{269643786736}{12794929} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -29 a - 5\) , \( -113 a + 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-29a-5\right){x}-113a+45$ |
| 18396.3-d2 |
18396.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.209103646$ |
$3.146761764$ |
3.039168860 |
\( -\frac{20198991}{14308} a + \frac{7397423}{14308} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( a - 5\) , \( -5 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-5\right){x}-5a+3$ |
| 18396.3-e1 |
18396.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{6} \cdot 3^{9} \cdot 7^{3} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.899085400$ |
2.076348791 |
\( \frac{91698753975}{50078} a - \frac{2663522590089}{200312} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -53 a + 294\) , \( 1854 a - 475\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-53a+294\right){x}+1854a-475$ |
| 18396.3-e2 |
18396.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.3 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{2} \cdot 3^{3} \cdot 7 \cdot 73^{3} \) |
$1.80252$ |
$(-2a+1), (3a-2), (-9a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.697256201$ |
2.076348791 |
\( \frac{5400420903}{5446238} a + \frac{2446870005}{5446238} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 2 a + 4\) , \( -2 a + 7\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+4\right){x}-2a+7$ |
*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.
