| 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 |
| 12100.1-a1 |
12100.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 5^{2} \cdot 11^{10} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 5 \) |
$1$ |
$0.275229175$ |
1.589036387 |
\( -\frac{23178622194826561}{1610510} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -5939 a + 5939\) , \( -172745\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-5939a+5939\right){x}-172745$ |
| 12100.1-a2 |
12100.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 5^{10} \cdot 11^{2} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$1.376145879$ |
1.589036387 |
\( \frac{109902239}{1100000} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 11 a - 11\) , \( -55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(11a-11\right){x}-55$ |
| 12100.1-b1 |
12100.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 5^{2} \cdot 11^{2} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$5.023922189$ |
1.933708552 |
\( -\frac{117649}{440} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}+1$ |
| 12100.1-b2 |
12100.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 5^{6} \cdot 11^{6} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1.674640729$ |
1.933708552 |
\( \frac{80062991}{332750} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 9\) , \( -25\bigr] \) |
${y}^2+{x}{y}={x}^{3}+9{x}-25$ |
| 12100.1-c1 |
12100.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{14} \cdot 5^{2} \cdot 11^{6} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$1.098979844$ |
2.960982774 |
\( -\frac{76711450249}{851840} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -89\) , \( 316\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-89{x}+316$ |
| 12100.1-c2 |
12100.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12100.1 |
\( 2^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 2^{42} \cdot 5^{6} \cdot 11^{2} \) |
$1.62329$ |
$(2), (5), (11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \cdot 7 \) |
$1$ |
$0.366326614$ |
2.960982774 |
\( \frac{2882081488391}{2883584000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 296\) , \( 1702\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+296{x}+1702$ |
*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.
