| 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 |
| 675.2-c5 |
675.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
675.2 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{26} \cdot 5^{2} \) |
$1.28828$ |
$(-a-1), (a-1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.936094769$ |
1.323837918 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -20 a - 53\) , \( -97 a - 129\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-53\right){x}-97a-129$ |
| 675.3-c5 |
675.3-c |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
675.3 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{26} \cdot 5^{2} \) |
$1.28828$ |
$(-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.936094769$ |
1.323837918 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -9 a + 59\) , \( 152 a + 25\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a+59\right){x}+152a+25$ |
| 10800.2-a5 |
10800.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10800.2 |
\( 2^{4} \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{26} \cdot 5^{2} \) |
$2.57656$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.533367785$ |
$0.468047384$ |
3.353768336 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -76 a - 214\) , \( -986 a - 880\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-76a-214\right){x}-986a-880$ |
| 10800.3-b5 |
10800.3-b |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
10800.3 |
\( 2^{4} \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{26} \cdot 5^{2} \) |
$2.57656$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.533367785$ |
$0.468047384$ |
3.353768336 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -36 a + 234\) , \( 986 a + 128\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-36a+234\right){x}+986a+128$ |
| 16875.2-c5 |
16875.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16875.2 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{26} \cdot 5^{14} \) |
$2.88068$ |
$(-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.187218953$ |
1.059070334 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -480 a - 1336\) , \( -14260 a - 12891\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-480a-1336\right){x}-14260a-12891$ |
| 16875.3-a5 |
16875.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16875.3 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{26} \cdot 5^{14} \) |
$2.88068$ |
$(-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.187218953$ |
1.059070334 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -221 a + 1464\) , \( 16360 a + 759\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-221a+1464\right){x}+16360a+759$ |
| 27225.4-a5 |
27225.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{20} \cdot 5^{2} \cdot 11^{6} \) |
$3.24658$ |
$(-a-1), (a-1), (a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.488859549$ |
0.691351805 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 82 a - 185\) , \( 526 a - 1154\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(82a-185\right){x}+526a-1154$ |
| 27225.6-a5 |
27225.6-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{20} \cdot 5^{2} \cdot 11^{6} \) |
$3.24658$ |
$(-a-1), (a-1), (a-3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.488859549$ |
0.691351805 |
\( \frac{4081867299328}{1937102445} a + \frac{194392780864}{1937102445} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 113 a + 151\) , \( 89 a - 1308\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(113a+151\right){x}+89a-1308$ |
*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.
