| 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 |
| 44100.1-a1 |
44100.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{9} \cdot 5^{2} \cdot 7^{8} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.724053152$ |
$0.504365807$ |
3.373459039 |
\( -\frac{387003}{1280} a + \frac{425487}{640} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 143 a - 31\) , \( -748 a + 868\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(143a-31\right){x}-748a+868$ |
| 44100.1-b1 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{6} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.282437263$ |
1.956782763 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 205 a + 121\) , \( -3500 a + 6873\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(205a+121\right){x}-3500a+6873$ |
| 44100.1-b2 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.847311791$ |
1.956782763 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -20 a - 14\) , \( 100 a - 228\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-14\right){x}+100a-228$ |
| 44100.1-b3 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{24} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.070609315$ |
1.956782763 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6805 a + 4081\) , \( -21740 a + 53553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6805a+4081\right){x}-21740a+53553$ |
| 44100.1-b4 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{30} \cdot 5^{2} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \) |
$1$ |
$0.211827947$ |
1.956782763 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 1030 a + 616\) , \( -9980 a + 20478\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1030a+616\right){x}-9980a+20478$ |
| 44100.1-b5 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \) |
$1$ |
$0.423655895$ |
1.956782763 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 280 a + 166\) , \( 2020 a - 3192\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(280a+166\right){x}+2020a-3192$ |
| 44100.1-b6 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{12} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.141218631$ |
1.956782763 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5005 a + 3001\) , \( -134060 a + 257817\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5005a+3001\right){x}-134060a+257817$ |
| 44100.1-b7 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{8} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1$ |
$0.211827947$ |
1.956782763 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4330 a + 2596\) , \( 118660 a - 211038\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4330a+2596\right){x}+118660a-211038$ |
| 44100.1-b8 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{14} \cdot 5^{6} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.070609315$ |
1.956782763 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 80005 a + 48001\) , \( -8894060 a + 16610817\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(80005a+48001\right){x}-8894060a+16610817$ |
| 44100.1-c1 |
44100.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{4} \) |
$0.042806680$ |
$2.311294492$ |
3.655831603 |
\( -\frac{387003}{1280} a + \frac{425487}{640} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -4 a - 4\) , \( -9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4a-4\right){x}-9$ |
| 44100.1-d1 |
44100.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{11} \cdot 5^{2} \cdot 7^{8} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.085141421$ |
$0.824125745$ |
3.889063064 |
\( \frac{404917}{270} a - \frac{123661}{540} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -65 a + 4\) , \( 142 a - 195\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-65a+4\right){x}+142a-195$ |
| 44100.1-e1 |
44100.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 7^{8} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.306829861$ |
3.017994289 |
\( \frac{152207}{196} a + \frac{317396}{245} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( a - 29\) , \( 12 a + 15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-29\right){x}+12a+15$ |
| 44100.1-e2 |
44100.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{4} \cdot 7^{10} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.653414930$ |
3.017994289 |
\( -\frac{1668770723}{24010} a + \frac{6868996887}{120050} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 91 a - 269\) , \( 750 a - 1659\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(91a-269\right){x}+750a-1659$ |
*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.
