| 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 |
| 363.1-a1 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{2} \) |
$1.78741$ |
$(-a+2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.883253066$ |
2.465757066 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -215 a + 613\) , \( 885 a - 2460\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-215a+613\right){x}+885a-2460$ |
| 363.1-a2 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{4} \) |
$1.78741$ |
$(-a+2), (11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$7.533012266$ |
2.465757066 |
\( \frac{169112377}{88209} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 60 a - 157\) , \( 115 a - 315\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(60a-157\right){x}+115a-315$ |
| 363.1-a3 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$1.78741$ |
$(-a+2), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$30.13204906$ |
2.465757066 |
\( \frac{30664297}{297} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 35 a - 87\) , \( -151 a + 428\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(35a-87\right){x}-151a+428$ |
| 363.1-a4 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.78741$ |
$(-a+2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.883253066$ |
2.465757066 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 735 a - 2047\) , \( 16369 a - 45702\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(735a-2047\right){x}+16369a-45702$ |
| 363.1-b1 |
363.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{2} \) |
$1.78741$ |
$(-a+2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.039211695$ |
$2.234063206$ |
1.481653873 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$ |
| 363.1-b2 |
363.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{4} \) |
$1.78741$ |
$(-a+2), (11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.519605847$ |
$8.936252827$ |
1.481653873 |
\( \frac{169112377}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$ |
| 363.1-b3 |
363.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$1.78741$ |
$(-a+2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.759802923$ |
$8.936252827$ |
1.481653873 |
\( \frac{30664297}{297} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$ |
| 363.1-b4 |
363.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.78741$ |
$(-a+2), (11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.759802923$ |
$8.936252827$ |
1.481653873 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
*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.
