| 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 |
| 27.2-a2 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4 a + 15\) , \( 8 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+15\right){x}+8a+3$ |
| 27.3-a2 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{18} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.289634401$ |
0.690350747 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6 a + 7\) , \( 16 a - 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+7\right){x}+16a-34$ |
| 675.4-c2 |
675.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.4 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$0.930300277$ |
$1.023955633$ |
2.297724390 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 42 a + 9\) , \( -44 a - 257\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(42a+9\right){x}-44a-257$ |
| 675.6-a2 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.023955633$ |
1.234936958 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -39 a - 23\) , \( -138 a + 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39a-23\right){x}-138a+63$ |
| 675.7-a2 |
675.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.7 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.023955633$ |
1.234936958 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 34 a - 72\) , \( -148 a + 120\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a-72\right){x}-148a+120$ |
| 675.9-c2 |
675.9-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.9 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.186060055$ |
$1.023955633$ |
2.297724390 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -39 a + 62\) , \( 24 a + 313\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-39a+62\right){x}+24a+313$ |
| 1089.2-c2 |
1089.2-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{6} \) |
$1.70252$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$1.195722568$ |
3.605239194 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 3 a + 54\) , \( -115 a + 86\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+54\right){x}-115a+86$ |
| 2304.2-d2 |
2304.2-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$2.113528035$ |
$0.991440778$ |
2.527193171 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 80\) , \( 60 a + 300\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-80\right){x}+60a+300$ |
| 2304.2-h2 |
2304.2-h |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.422705607$ |
$0.991440778$ |
2.527193171 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 80\) , \( -60 a - 300\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-80\right){x}-60a-300$ |
| 4761.4-b2 |
4761.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.4 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{12} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.826918772$ |
2.493253908 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -52 a - 56\) , \( -296 a - 30\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-52a-56\right){x}-296a-30$ |
| 4761.6-b2 |
4761.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.6 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{12} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.826918772$ |
2.493253908 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 39 a - 117\) , \( -267 a + 433\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(39a-117\right){x}-267a+433$ |
| 6912.2-n2 |
6912.2-n |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{18} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$3.716380344$ |
$0.572408600$ |
5.131211894 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -69 a + 252\) , \( -647 a - 583\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-69a+252\right){x}-647a-583$ |
| 6912.3-r2 |
6912.3-r |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{18} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.743276068$ |
$0.572408600$ |
5.131211894 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 94 a + 143\) , \( -513 a + 1715\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(94a+143\right){x}-513a+1715$ |
| 8649.4-c2 |
8649.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.4 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{12} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (-3a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1.244671488$ |
$0.712272081$ |
5.346066004 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 83 a + 39\) , \( 46 a + 724\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(83a+39\right){x}+46a+724$ |
| 8649.6-c2 |
8649.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.6 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{12} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$6.223357440$ |
$0.712272081$ |
5.346066004 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -71 a + 143\) , \( -181 a - 668\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-71a+143\right){x}-181a-668$ |
| 9801.3-l2 |
9801.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{6} \) |
$2.94885$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.398574189$ |
0.961397118 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 31 a + 492\) , \( 2584 a - 2235\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(31a+492\right){x}+2584a-2235$ |
| 16875.13-bc1 |
16875.13-bc |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.311993371$ |
$0.457926880$ |
6.892315432 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 147 a + 224\) , \( 853 a - 3073\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(147a+224\right){x}+853a-3073$ |
| 16875.8-ba1 |
16875.8-ba |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{18} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{7} \) |
$1.559966858$ |
$0.457926880$ |
6.892315432 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -109 a + 394\) , \( 1505 a + 1284\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-109a+394\right){x}+1505a+1284$ |
| 19881.4-a1 |
19881.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.4 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{12} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (-2a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.578466002$ |
0.348828124 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 115 a - 204\) , \( -926 a + 983\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(115a-204\right){x}-926a+983$ |
| 19881.6-b1 |
19881.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.6 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{12} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.578466002$ |
0.348828124 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -130 a - 40\) , \( -779 a + 547\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-130a-40\right){x}-779a+547$ |
| 20736.3-bi1 |
20736.3-bi |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{24} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.330480259$ |
3.188593517 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a - 714\) , \( -820 a - 7510\bigr] \) |
${y}^2={x}^{3}+\left(-45a-714\right){x}-820a-7510$ |
| 20736.3-bl1 |
20736.3-bl |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{24} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.330480259$ |
3.188593517 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -45 a - 714\) , \( 820 a + 7510\bigr] \) |
${y}^2={x}^{3}+\left(-45a-714\right){x}+820a+7510$ |
| 27225.4-f1 |
27225.4-f |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \cdot 5 \) |
$0.284422680$ |
$0.534743389$ |
3.668624767 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 166 a - 142\) , \( 1009 a + 71\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(166a-142\right){x}+1009a+71$ |
| 27225.6-c1 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \) |
$1.422113402$ |
$0.534743389$ |
3.668624767 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -171 a + 85\) , \( 750 a - 1899\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-171a+85\right){x}+750a-1899$ |
| 31329.4-b1 |
31329.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.4 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{12} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.516298381$ |
1.556698190 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -94 a - 215\) , \( -993 a - 862\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-94a-215\right){x}-993a-862$ |
| 31329.6-b1 |
31329.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.6 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{12} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a-8)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.516298381$ |
1.556698190 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 60 a - 317\) , \( -585 a + 2135\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(60a-317\right){x}-585a+2135$ |
| 36864.2-t1 |
36864.2-t |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{12} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$13.99529155$ |
$0.495720389$ |
8.367242985 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -19 a - 318\) , \( -124 a - 2139\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a-318\right){x}-124a-2139$ |
| 36864.2-bg1 |
36864.2-bg |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{12} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$2.799058310$ |
$0.495720389$ |
8.367242985 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -19 a - 318\) , \( 124 a + 2139\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a-318\right){x}+124a+2139$ |
| 36963.4-a1 |
36963.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.4 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{18} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$4.339882007$ |
$0.376413576$ |
3.940368569 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 340 a - 93\) , \( -1860 a - 4140\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(340a-93\right){x}-1860a-4140$ |
| 36963.6-a1 |
36963.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.6 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{18} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \) |
$9.209082879$ |
$0.376413576$ |
8.361328871 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -233 a - 303\) , \( -2954 a - 698\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-233a-303\right){x}-2954a-698$ |
| 36963.7-a1 |
36963.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.7 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{18} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$1.841816575$ |
$0.376413576$ |
8.361328871 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 177 a - 578\) , \( -2484 a + 4722\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(177a-578\right){x}-2484a+4722$ |
| 36963.9-a1 |
36963.9-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.9 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{18} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.867976401$ |
$0.376413576$ |
3.940368569 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -324 a + 352\) , \( -860 a + 5381\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-324a+352\right){x}-860a+5381$ |
| 40401.4-a1 |
40401.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.4 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{12} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (-3a-5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$2.331249060$ |
$0.484495076$ |
6.811012775 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -205 a + 43\) , \( 1245 a - 1654\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-205a+43\right){x}+1245a-1654$ |
| 40401.6-a1 |
40401.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.6 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{12} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (3a-8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$11.65624530$ |
$0.484495076$ |
6.811012775 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 193 a - 221\) , \( 1590 a - 94\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(193a-221\right){x}+1590a-94$ |
| 42849.7-c1 |
42849.7-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.7 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{24} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.275639590$ |
0.664867708 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -464 a - 504\) , \( 7985 a + 831\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-464a-504\right){x}+7985a+831$ |
| 42849.9-d1 |
42849.9-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.9 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{24} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.275639590$ |
0.664867708 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 364 a - 1058\) , \( 6130 a - 11714\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(364a-1058\right){x}+6130a-11714$ |
| 45369.4-a1 |
45369.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.4 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{12} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (-5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.470649492$ |
0.283812322 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -56 a + 380\) , \( 1638 a + 320\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-56a+380\right){x}+1638a+320$ |
| 45369.6-a1 |
45369.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.6 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{12} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (5a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.470649492$ |
0.283812322 |
\( \frac{349209575}{59049} a - \frac{1245002978}{59049} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 97 a + 279\) , \( 1316 a - 2328\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(97a+279\right){x}+1316a-2328$ |
*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.
