| 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 |
| 97344.2-a1 |
97344.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 13^{5} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.420273948$ |
$2.047453076$ |
5.815888530 |
\( -\frac{4141815344}{85683} a - \frac{4891425528}{28561} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 16 i + 24\) , \( -23 i + 44\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(16i+24\right){x}-23i+44$ |
| 97344.2-a2 |
97344.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 13^{5} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.420273948$ |
$2.047453076$ |
5.815888530 |
\( \frac{4141815344}{85683} a - \frac{4891425528}{28561} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -15 i + 24\) , \( 47 i + 59\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-15i+24\right){x}+47i+59$ |
| 97344.2-a3 |
97344.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{4} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.355068487$ |
$2.047453076$ |
5.815888530 |
\( \frac{778688}{1521} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -8\) , \( -10 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-8{x}-10i$ |
| 97344.2-a4 |
97344.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{2} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.355068487$ |
$2.047453076$ |
5.815888530 |
\( \frac{5088448}{1053} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -14\) , \( 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-14{x}+12$ |
| 97344.2-b1 |
97344.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 13^{2} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.728094279$ |
$0.717282506$ |
5.870442907 |
\( -\frac{245314376}{6908733} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 26\) , \( 357 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+26{x}+357i$ |
| 97344.2-b2 |
97344.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 13^{8} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.170505892$ |
$0.717282506$ |
5.870442907 |
\( \frac{1360251712}{771147} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 92\) , \( 18 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+92{x}+18i$ |
| 97344.2-b3 |
97344.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 13^{4} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.682023569$ |
$0.717282506$ |
5.870442907 |
\( \frac{22235451328}{123201} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -234\) , \( 1296\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-234{x}+1296$ |
| 97344.2-b4 |
97344.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 13^{2} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$2.728094279$ |
$0.717282506$ |
5.870442907 |
\( \frac{11339065490696}{351} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 936\) , \( 10867 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+936\right){x}+10867i$ |
| 97344.2-c1 |
97344.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 13^{2} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.320299800$ |
$0.711431615$ |
4.557428092 |
\( \frac{1643032000}{767637} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -98\) , \( 132\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-98{x}+132$ |
| 97344.2-c2 |
97344.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 13^{4} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.160149900$ |
$0.711431615$ |
4.557428092 |
\( \frac{61162984000}{41067} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 328\) , \( -2398 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+328{x}-2398i$ |
| 97344.2-d1 |
97344.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 13^{4} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.266481163$ |
$2.420020004$ |
5.159117971 |
\( \frac{1000000}{507} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( -6 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+8{x}-6i$ |
| 97344.2-d2 |
97344.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{2} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.532962326$ |
$2.420020004$ |
5.159117971 |
\( \frac{10648000}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -18\) , \( -36\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-18{x}-36$ |
| 97344.2-e1 |
97344.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 13^{15} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.250676465$ |
4.010823441 |
\( -\frac{1036815206125907888}{209682766102329} a - \frac{132926443011554808}{23298085122481} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -1035 i + 46\) , \( 9511 i - 9373\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-1035i+46\right){x}+9511i-9373$ |
| 97344.2-e2 |
97344.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 13^{15} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.250676465$ |
4.010823441 |
\( \frac{1036815206125907888}{209682766102329} a - \frac{132926443011554808}{23298085122481} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 1036 i + 46\) , \( -9465 i - 10408\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(1036i+46\right){x}-9465i-10408$ |
| 97344.2-e3 |
97344.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{12} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.250676465$ |
4.010823441 |
\( -\frac{420526439488}{390971529} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 624\) , \( 9486 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+624{x}+9486i$ |
| 97344.2-e4 |
97344.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
97344.2 |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 13^{6} \) |
$3.15679$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.250676465$ |
4.010823441 |
\( \frac{42246001231552}{14414517} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2902\) , \( -61132\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2902{x}-61132$ |
*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.
