| 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 |
| 2704.2-b1 |
2704.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2704.2 |
\( 2^{4} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{4} \) |
$1.28875$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.044031078$ |
$3.096799887$ |
1.636265263 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -6 i - 2\) , \( 4 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-6i-2\right){x}+4i-4$ |
| 17576.2-a1 |
17576.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
17576.2 |
\( 2^{3} \cdot 13^{3} \) |
\( 2^{10} \cdot 13^{10} \) |
$2.05778$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$0.203889286$ |
$0.858897752$ |
2.801920801 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -i - 79\) , \( 70 i + 303\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-i-79\right){x}+70i+303$ |
| 17576.3-b1 |
17576.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
17576.3 |
\( 2^{3} \cdot 13^{3} \) |
\( 2^{10} \cdot 13^{10} \) |
$2.05778$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.526688343$ |
$0.858897752$ |
3.618971473 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -56 i + 57\) , \( 165 i + 207\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-56i+57\right){x}+165i+207$ |
| 33800.2-g1 |
33800.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.2 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{6} \cdot 13^{4} \) |
$2.42325$ |
$(a+1), (-a-2), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.384931012$ |
2.769862024 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 25 i - 16\) , \( 68 i - 10\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(25i-16\right){x}+68i-10$ |
| 33800.8-e1 |
33800.8-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{6} \cdot 13^{4} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.248221662$ |
$1.384931012$ |
4.125238536 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 6 i + 29\) , \( -45 i + 23\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(6i+29\right){x}-45i+23$ |
| 43264.2-g1 |
43264.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{22} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.548399943$ |
3.096799887 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -22 i - 9\) , \( 55 i - 23\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-22i-9\right){x}+55i-23$ |
*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.
