| 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 |
| 30000.1-c2 |
30000.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30000.1 |
\( 2^{4} \cdot 3 \cdot 5^{4} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{16} \) |
$2.03695$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.360141112$ |
2.495130817 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -333 a + 333\) , \( -3537\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-333a+333\right){x}-3537$ |
| 22500.3-f2 |
22500.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{16} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$0.286792415$ |
$0.720282224$ |
3.718286617 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 83\) , \( 400 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+83{x}+400i$ |
| 22500.2-f2 |
22500.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{16} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$0.720282224$ |
4.583848008 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -83\) , \( 401\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-83{x}+401$ |
| 900.2-c2 |
900.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{4} \) |
$2.18884$ |
$(2,a+1), (3,a+1), (3,a+2), (-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$0.159999281$ |
$3.601411123$ |
4.638507206 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( 23\bigr] \) |
${y}^2={x}^3+{x}^2-13{x}+23$ |
| 900.1-b2 |
900.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \) |
$3.09549$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$3.601411123$ |
3.416598582 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -3\) , \( 7\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-3{x}+7$ |
| 300.1-h2 |
300.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \) |
$4.07389$ |
$(2,a), (3,a), (5,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$3.601411123$ |
3.945148222 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( 100\bigr] \) |
${y}^2+a{y}={x}^3-30{x}+100$ |
| 3600.1-a2 |
3600.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{4} \) |
$1.54774$ |
$(-2a+1), (2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.472283883$ |
1.975276106 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( -23\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}-23$ |
| 27.1-d2 |
27.1-d |
$2$ |
$3$ |
3.3.1300.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$5.58047$ |
$(3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3 \) |
$1$ |
$15.97836473$ |
1.329480307 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( a^{2} - 6\) , \( a + 1\) , \( -a^{2} + 3 a + 12\) , \( -2 a - 6\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-a^{2}+3a+12\right){x}-2a-6$ |
*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.
