| 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 |
| 44.3-a1 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( \frac{2775668240489}{85184} a - \frac{3929396676037}{42592} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -55 a + 91\) , \( 87 a + 359\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-55a+91\right){x}+87a+359$ |
| 44.3-a2 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{7} \cdot 11^{12} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.840444112$ |
0.635316032 |
\( -\frac{41728910180660407}{200859416110144} a - \frac{5044929390482523}{100429708055072} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -4 a + 40\) , \( 135 a + 83\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4a+40\right){x}+135a+83$ |
| 44.3-a3 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{2222449}{45056} a + \frac{42043605}{45056} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$ |
| 44.3-a4 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{25} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( -\frac{74168468086089}{22330474496} a + \frac{45400743717419}{11165237248} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 14 a - 17\) , \( -19 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-17\right){x}-19a+5$ |
| 44.3-a5 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( -\frac{998361}{7744} a + \frac{23448551}{7744} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( a\) , \( 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}+1$ |
| 44.3-a6 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11^{6} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( \frac{49453830610989}{7256313856} a - \frac{991801247255}{3628156928} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -14 a - 10\) , \( 27 a - 9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14a-10\right){x}+27a-9$ |
| 44.3-a7 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{11} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{7153263}{2816} a + \frac{40910099}{1408} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( -3 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+3\right){x}-3a+1$ |
| 44.3-a8 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.521332337$ |
0.635316032 |
\( -\frac{67333244623}{117128} a + \frac{557731279327}{117128} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 21 a\) , \( 20 a + 57\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+21a{x}+20a+57$ |
*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.
