| 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 |
| 22500.3-a1 |
22500.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{11} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.176732339$ |
$1.590905565$ |
3.373973544 |
\( -\frac{5972768}{75} a - \frac{5804176}{75} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -38 i - 21\) , \( 96 i - 3\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-38i-21\right){x}+96i-3$ |
| 22500.3-a2 |
22500.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{10} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.088366169$ |
$1.590905565$ |
3.373973544 |
\( -\frac{4096}{45} a + \frac{4096}{15} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 4 i + 10\) , \( 14 i + 21\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(4i+10\right){x}+14i+21$ |
| 22500.3-b1 |
22500.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{11} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.176732339$ |
$1.590905565$ |
3.373973544 |
\( \frac{5972768}{75} a - \frac{5804176}{75} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 38 i - 21\) , \( -96 i - 3\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(38i-21\right){x}-96i-3$ |
| 22500.3-b2 |
22500.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{10} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.088366169$ |
$1.590905565$ |
3.373973544 |
\( \frac{4096}{45} a + \frac{4096}{15} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -4 i + 10\) , \( 14 i - 21\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-4i+10\right){x}+14i-21$ |
| 22500.3-c1 |
22500.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.479997843$ |
$1.200470374$ |
3.457339142 |
\( -\frac{30866268160}{3} \) |
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 303\) , \( -2135 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+303{x}-2135i$ |
| 22500.3-c2 |
22500.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.159999281$ |
$3.601411123$ |
3.457339142 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 3\) , \( -5 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+3{x}-5i$ |
| 22500.3-d1 |
22500.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{6} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.060591966$ |
$2.388115705$ |
3.472815038 |
\( \frac{5488}{81} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -3\) , \( 9 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-3{x}+9i$ |
| 22500.3-d2 |
22500.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.121183932$ |
$2.388115705$ |
3.472815038 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+22$ |
| 22500.3-e1 |
22500.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{18} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.964415679$ |
$0.477623141$ |
3.685017969 |
\( \frac{5488}{81} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 73\) , \( 1198 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i-73\right){x}+1198i$ |
| 22500.3-e2 |
22500.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{18} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.928831358$ |
$0.477623141$ |
3.685017969 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -333\) , \( 2088\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-333{x}+2088$ |
| 22500.3-f1 |
22500.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{16} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$0.860377245$ |
$0.240094074$ |
3.718286617 |
\( -\frac{30866268160}{3} \) |
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 7583\) , \( 251650 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+7583{x}+251650i$ |
| 22500.3-f2 |
22500.3-f |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{16} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$0.286792415$ |
$0.720282224$ |
3.718286617 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -i\) , \( i + 1\) , \( 83\) , \( 400 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+83{x}+400i$ |
*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.
