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 |
147.2-a1 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{20} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.431038464$ |
0.497720347 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-470a+321\right){x}+1866a-3772$ |
3087.2-a1 |
3087.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.2 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{7} \cdot 7^{26} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.094060304$ |
1.737783746 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 3474 a + 6465\) , \( -321486 a + 306732\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(3474a+6465\right){x}-321486a+306732$ |
3087.3-a1 |
3087.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3087.3 |
\( 3^{2} \cdot 7^{3} \) |
\( 3^{7} \cdot 7^{26} \) |
$1.15367$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.094060304$ |
1.737783746 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -654 a - 8391\) , \( 19194 a + 304332\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-654a-8391\right){x}+19194a+304332$ |
7203.3-a1 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3 \cdot 7^{32} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.277017646$ |
$0.061576923$ |
1.500845174 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -23030 a + 15728\) , \( -663068 a + 1309524\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-23030a+15728\right){x}-663068a+1309524$ |
24843.4-b5 |
24843.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.4 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1055 a - 4803\) , \( -36894 a - 131300\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1055a-4803\right){x}-36894a-131300$ |
24843.6-b5 |
24843.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
24843.6 |
\( 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 3 \cdot 7^{20} \cdot 13^{6} \) |
$1.94312$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.119548560$ |
2.208684594 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6007 a + 1525\) , \( 167514 a - 132740\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6007a+1525\right){x}+167514a-132740$ |
37632.2-f5 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3 \cdot 7^{20} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.492598417$ |
$0.107759616$ |
2.971586411 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7520 a + 5136\) , \( -119424 a + 241408\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-7520a+5136\right){x}-119424a+241408$ |
91875.2-c5 |
91875.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91875.2 |
\( 3 \cdot 5^{4} \cdot 7^{2} \) |
\( 3 \cdot 5^{12} \cdot 7^{20} \) |
$2.69463$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.472574897$ |
$0.086207692$ |
3.010689818 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 8025 a + 3724\) , \( 245000 a - 479525\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(8025a+3724\right){x}+245000a-479525$ |
112896.2-q5 |
112896.2-q |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{7} \cdot 7^{20} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$1$ |
$0.062215043$ |
2.298871812 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 22561 a - 15407\) , \( 1083023 a + 14880\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(22561a-15407\right){x}+1083023a+14880$ |
112896.2-y5 |
112896.2-y |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{7} \cdot 7^{20} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.062215043$ |
2.298871812 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22561 a - 15407\) , \( -1083023 a - 14880\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(22561a-15407\right){x}-1083023a-14880$ |
*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.