| 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 |
| 100.2-a1 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( -\frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 4 i - 11\) , \( 11 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(4i-11\right){x}+11i-12$ |
| 100.2-a2 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( \frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -6 i - 11\) , \( -12 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-6i-11\right){x}-12i-12$ |
| 100.2-a3 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{15} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.070515942$ |
0.535257971 |
\( -\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 54 i - 1\) , \( -119 i - 118\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(54i-1\right){x}-119i-118$ |
| 100.2-a4 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{15} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.070515942$ |
0.535257971 |
\( \frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -56 i - 1\) , \( 118 i - 118\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-56i-1\right){x}+118i-118$ |
| 100.2-a5 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.141031885$ |
0.535257971 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 9\) , \( 17 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+9\right){x}+17i$ |
| 100.2-a6 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}-i$ |
| 100.2-a7 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.2-a8 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.141031885$ |
0.535257971 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
*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.
