| 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 |
| 72200.2-a1 |
72200.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 19^{2} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.215701219$ |
$1.850869842$ |
6.387758125 |
\( -\frac{55296}{11875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 21\bigr] \) |
${y}^2={x}^{3}-2{x}+21$ |
| 72200.2-a2 |
72200.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 19^{8} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.451219517$ |
$0.925434921$ |
6.387758125 |
\( \frac{1263284964}{651605} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 56\) , \( -26 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+56{x}-26i$ |
| 72200.2-a3 |
72200.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 19^{4} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.862804879$ |
$1.850869842$ |
6.387758125 |
\( \frac{884901456}{9025} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 31\) , \( 84 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+31{x}+84i$ |
| 72200.2-a4 |
72200.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 19^{2} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.451219517$ |
$0.925434921$ |
6.387758125 |
\( \frac{899466517764}{95} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 506\) , \( 4644 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+506{x}+4644i$ |
| 72200.2-b1 |
72200.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{28} \cdot 19^{2} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7^{2} \) |
$0.296696420$ |
$0.077929846$ |
4.531815283 |
\( -\frac{121981271658244096}{115966796875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -26035\) , \( -1626942\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-26035{x}-1626942$ |
| 72200.2-b2 |
72200.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 5^{14} \cdot 19^{4} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$0.593392841$ |
$0.077929846$ |
4.531815283 |
\( \frac{31248575021659890256}{28203125} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 104165\) , \( -12957274 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+104165{x}-12957274i$ |
| 72200.2-c1 |
72200.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 19^{2} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.429803034$ |
$3.105934259$ |
5.339759879 |
\( \frac{702464}{475} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+5{x}$ |
| 72200.2-c2 |
72200.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 19^{4} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.859606069$ |
$3.105934259$ |
5.339759879 |
\( \frac{3631696}{1805} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 5\) , \( 2 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+5\right){x}+2i$ |
| 72200.2-d1 |
72200.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 19^{2} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.108846514$ |
$1.353154244$ |
5.302300421 |
\( \frac{91765424}{296875} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -15\) , \( 50 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}-15{x}+50i$ |
| 72200.2-d2 |
72200.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 19^{4} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.217693028$ |
$1.353154244$ |
5.302300421 |
\( \frac{304900096}{45125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -35\) , \( 58\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-35{x}+58$ |
| 72200.2-e1 |
72200.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72200.2 |
\( 2^{3} \cdot 5^{2} \cdot 19^{2} \) |
\( 2^{10} \cdot 5^{4} \cdot 19^{6} \) |
$2.92956$ |
$(a+1), (-a-2), (2a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.109123604$ |
$1.050674755$ |
5.503363984 |
\( -\frac{16241202}{171475} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 16\) , \( -108 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+16\right){x}-108i$ |
*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.
