| 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 |
| 6084.2-a1 |
6084.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{4} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.073707206$ |
$3.590171887$ |
1.587729233 |
\( \frac{3631696}{507} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 5\) , \( 3 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+5{x}+3i$ |
| 6084.2-a2 |
6084.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.147414412$ |
$3.590171887$ |
1.587729233 |
\( \frac{1048576}{117} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5{x}+6$ |
| 6084.2-b1 |
6084.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.331439434$ |
$1.882955324$ |
2.507040972 |
\( \frac{16384000}{9477} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+4$ |
| 6084.2-b2 |
6084.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{12} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.221906572$ |
$0.627651774$ |
2.507040972 |
\( \frac{181037698000}{14480427} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 187\) , \( 945 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+187\right){x}+945i$ |
| 6084.2-b3 |
6084.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.665719717$ |
$1.882955324$ |
2.507040972 |
\( \frac{1409938000}{4563} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 37\) , \( -81 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+37\right){x}-81i$ |
| 6084.2-b4 |
6084.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6084.2 |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{6} \) |
$1.57840$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.443813144$ |
$0.627651774$ |
2.507040972 |
\( \frac{2725888000000}{19773} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -733\) , \( 7888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-733{x}+7888$ |
*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.
