| 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 |
| 12800.2-c1 |
12800.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.2 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{17} \cdot 5^{10} \) |
$1.90095$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.303357396$ |
$1.269781619$ |
3.081581164 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -2 i + 35\) , \( 83 i + 1\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-2i+35\right){x}+83i+1$ |
| 12800.2-e1 |
12800.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.2 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{17} \cdot 5^{10} \) |
$1.90095$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.213429584$ |
$1.269781619$ |
3.081581164 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i - 35\) , \( -i + 83\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i-35\right){x}-i+83$ |
| 25600.2-b1 |
25600.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{23} \cdot 5^{10} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.897871193$ |
1.795742386 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 70 i + 5\) , \( 159 i + 238\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(70i+5\right){x}+159i+238$ |
| 25600.2-r1 |
25600.2-r |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{23} \cdot 5^{10} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.559256688$ |
$0.897871193$ |
4.017123764 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -70 i - 5\) , \( 238 i - 159\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-70i-5\right){x}+238i-159$ |
| 64000.2-b1 |
64000.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64000.2 |
\( 2^{9} \cdot 5^{3} \) |
\( 2^{17} \cdot 5^{16} \) |
$2.84259$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.567863603$ |
1.135727206 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -132 i - 116\) , \( 1044 i + 292\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-132i-116\right){x}+1044i+292$ |
| 64000.2-k1 |
64000.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64000.2 |
\( 2^{9} \cdot 5^{3} \) |
\( 2^{17} \cdot 5^{16} \) |
$2.84259$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.567863603$ |
2.271454413 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 132 i + 116\) , \( 292 i - 1044\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(132i+116\right){x}+292i-1044$ |
| 64000.3-c1 |
64000.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64000.3 |
\( 2^{9} \cdot 5^{3} \) |
\( 2^{17} \cdot 5^{16} \) |
$2.84259$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.567863603$ |
1.135727206 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -148 i + 94\) , \( 8 i + 1010\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-148i+94\right){x}+8i+1010$ |
| 64000.3-l1 |
64000.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64000.3 |
\( 2^{9} \cdot 5^{3} \) |
\( 2^{17} \cdot 5^{16} \) |
$2.84259$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.567863603$ |
2.271454413 |
\( -\frac{324134216}{390625} a - \frac{1619282312}{390625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 148 i - 94\) , \( 1010 i - 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(148i-94\right){x}+1010i-8$ |
*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.
