| 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 |
| 14256.3-a1 |
14256.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{17} \cdot 11 \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.623283383$ |
$0.672989763$ |
3.035350913 |
\( \frac{136606336}{891} a - \frac{93881776}{891} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 45 a + 249\) , \( -1008 a + 1222\bigr] \) |
${y}^2={x}^{3}+\left(45a+249\right){x}-1008a+1222$ |
| 14256.3-a2 |
14256.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{8} \cdot 3^{16} \cdot 11^{2} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.311641691$ |
$1.345979526$ |
3.035350913 |
\( \frac{131072}{99} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24\) , \( 25\bigr] \) |
${y}^2={x}^{3}+24{x}+25$ |
| 14256.3-a3 |
14256.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{14} \cdot 11^{4} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.155820845$ |
$0.672989763$ |
3.035350913 |
\( \frac{810448}{363} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 214\bigr] \) |
${y}^2={x}^{3}-111{x}+214$ |
| 14256.3-a4 |
14256.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{17} \cdot 11 \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.623283383$ |
$0.672989763$ |
3.035350913 |
\( -\frac{136606336}{891} a + \frac{14241520}{297} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a + 294\) , \( 1008 a + 214\bigr] \) |
${y}^2={x}^{3}+\left(-45a+294\right){x}+1008a+214$ |
| 14256.3-b1 |
14256.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{8} \cdot 3^{32} \cdot 11^{2} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.290488615$ |
1.051027354 |
\( -\frac{3196715008}{649539} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -696\) , \( -8215\bigr] \) |
${y}^2={x}^{3}-696{x}-8215$ |
| 14256.3-b2 |
14256.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{37} \cdot 11 \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.145244307$ |
1.051027354 |
\( \frac{14803409477504}{38354628411} a - \frac{33890549797520}{12784876137} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1395 a + 249\) , \( 29232 a - 44314\bigr] \) |
${y}^2={x}^{3}+\left(-1395a+249\right){x}+29232a-44314$ |
| 14256.3-b3 |
14256.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{37} \cdot 11 \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.145244307$ |
1.051027354 |
\( -\frac{14803409477504}{38354628411} a - \frac{86868239915056}{38354628411} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1395 a - 1146\) , \( -29232 a - 15082\bigr] \) |
${y}^2={x}^{3}+\left(1395a-1146\right){x}-29232a-15082$ |
| 14256.3-b4 |
14256.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{22} \cdot 11^{4} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.145244307$ |
1.051027354 |
\( \frac{932410994128}{29403} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11631\) , \( -482794\bigr] \) |
${y}^2={x}^{3}-11631{x}-482794$ |
| 14256.3-c1 |
14256.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{12} \cdot 11^{6} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.409574310$ |
4.445686838 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -696\) , \( 7108\bigr] \) |
${y}^2={x}^{3}-696{x}+7108$ |
| 14256.3-c2 |
14256.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14256.3 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{16} \cdot 3^{12} \cdot 11^{2} \) |
$3.23843$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.228722931$ |
4.445686838 |
\( \frac{8192}{11} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 24\) , \( 52\bigr] \) |
${y}^2={x}^{3}+24{x}+52$ |
*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.
