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 |
22500.2-a1 |
22500.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{6} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.119882568$ |
$2.388115705$ |
4.858560858 |
\( \frac{5488}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3\) , \( -9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+3{x}-9$ |
22500.2-a2 |
22500.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.119882568$ |
$2.388115705$ |
4.858560858 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+22$ |
22500.2-b1 |
22500.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$1.200470374$ |
2.546582227 |
\( -\frac{30866268160}{3} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -303\) , \( 2135\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-303{x}+2135$ |
22500.2-b2 |
22500.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$3.601411123$ |
2.546582227 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -3\) , \( 5\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-3{x}+5$ |
22500.2-c1 |
22500.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{16} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.655038515$ |
$0.550455002$ |
4.402226540 |
\( \frac{20283392}{6075} a - \frac{5636096}{6075} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -100 a - 134\) , \( 724 a + 275\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-100a-134\right){x}+724a+275$ |
22500.2-c2 |
22500.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{14} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.827519257$ |
$0.550455002$ |
4.402226540 |
\( -\frac{171491008}{295245} a - \frac{176375504}{295245} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -26 a + 124\) , \( -407 a - 617\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a+124\right){x}-407a-617$ |
22500.2-d1 |
22500.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{16} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.655038515$ |
$0.550455002$ |
4.402226540 |
\( -\frac{20283392}{6075} a - \frac{5636096}{6075} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 100 a - 134\) , \( -724 a + 275\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(100a-134\right){x}-724a+275$ |
22500.2-d2 |
22500.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{14} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.827519257$ |
$0.550455002$ |
4.402226540 |
\( \frac{171491008}{295245} a - \frac{176375504}{295245} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 26 a + 124\) , \( 407 a - 617\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(26a+124\right){x}+407a-617$ |
22500.2-e1 |
22500.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{18} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.477623141$ |
2.701844495 |
\( \frac{5488}{81} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 74\) , \( -1198\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+74{x}-1198$ |
22500.2-e2 |
22500.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{18} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.477623141$ |
2.701844495 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -333\) , \( 2088\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-333{x}+2088$ |
22500.2-f1 |
22500.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{16} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$0.240094074$ |
4.583848008 |
\( -\frac{30866268160}{3} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7583\) , \( 251651\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-7583{x}+251651$ |
22500.2-f2 |
22500.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{16} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$0.720282224$ |
4.583848008 |
\( -\frac{40960}{27} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -83\) , \( 401\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-83{x}+401$ |
*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.