| 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 |
| 33800.8-a1 |
33800.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{7} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.294552901$ |
$0.578523154$ |
2.995715314 |
\( \frac{21862400}{28561} a + \frac{29892608}{28561} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 128 i - 8\) , \( -528 i + 115\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(128i-8\right){x}-528i+115$ |
| 33800.8-a2 |
33800.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{9} \cdot 13^{8} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.647276450$ |
$0.578523154$ |
2.995715314 |
\( -\frac{6308647328}{4826809} a + \frac{9699305648}{4826809} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 145 i + 41\) , \( -48 i - 524\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(145i+41\right){x}-48i-524$ |
| 33800.8-b1 |
33800.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{18} \cdot 13^{5} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.127434599$ |
$0.121241088$ |
3.280593557 |
\( -\frac{12562530471206223672}{536376953125} a - \frac{4337347173715555804}{536376953125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -16197 i + 857\) , \( 521688 i - 597117\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-16197i+857\right){x}+521688i-597117$ |
| 33800.8-b2 |
33800.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{14} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1.127434599$ |
$0.121241088$ |
3.280593557 |
\( -\frac{13651818501408057352}{2912260640310125} a - \frac{8703911262017248564}{2912260640310125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -2497 i - 3293\) , \( -85724 i - 70383\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-2497i-3293\right){x}-85724i-70383$ |
| 33800.8-b3 |
33800.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{10} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.563717299$ |
$0.242482177$ |
3.280593557 |
\( \frac{303358645539264}{75418890625} a - \frac{163513993683952}{75418890625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -987 i + 12\) , \( 8097 i - 10180\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-987i+12\right){x}+8097i-10180$ |
| 33800.8-b4 |
33800.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{11} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.281858649$ |
$0.242482177$ |
3.280593557 |
\( -\frac{83684333293568}{101966340125} a - \frac{102316354533376}{101966340125} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -236 i - 665\) , \( -3091 i - 10247\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-236i-665\right){x}-3091i-10247$ |
| 33800.8-c1 |
33800.8-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 13^{8} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.118179007$ |
$1.397809941$ |
3.303835842 |
\( -\frac{2325317632}{371293} a + \frac{1271875584}{371293} \) |
\( \bigl[0\) , \( 1\) , \( i + 1\) , \( 29 i - 16\) , \( 79 i + 4\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(29i-16\right){x}+79i+4$ |
| 33800.8-d1 |
33800.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{9} \cdot 13^{6} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.559385163$ |
2.237540653 |
\( -\frac{58185123}{28561} a + \frac{207521489}{28561} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -113 i + 179\) , \( 654 i + 891\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-113i+179\right){x}+654i+891$ |
| 33800.8-d2 |
33800.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{3} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.118770326$ |
2.237540653 |
\( \frac{389018}{169} a + \frac{1352776}{169} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -23 i + 49\) , \( -110 i - 61\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-23i+49\right){x}-110i-61$ |
| 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 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 6 i + 29\) , \( -45 i + 23\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(6i+29\right){x}-45i+23$ |
| 33800.8-f1 |
33800.8-f |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 13^{2} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.146157372$ |
$2.457669850$ |
4.310478812 |
\( \frac{2048}{13} a + \frac{6144}{13} \) |
\( \bigl[0\) , \( -i - 1\) , \( i + 1\) , \( 5 i + 3\) , \( -10 i - 2\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(5i+3\right){x}-10i-2$ |
| 33800.8-g1 |
33800.8-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{6} \cdot 13^{4} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.384931012$ |
2.769862024 |
\( -\frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -27 i - 16\) , \( 68 i + 10\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-27i-16\right){x}+68i+10$ |
*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.
