| 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 |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
1.354107460 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
1.354107460 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
1.354107460 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.19516$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.141031885$ |
1.354107460 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.137812304$ |
$2.141031885$ |
1.679514028 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5\) , \( 25\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-5{x}+25$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.413436914$ |
$6.423095656$ |
1.679514028 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 5\) , \( -3\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+5{x}-3$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.826873828$ |
$6.423095656$ |
1.679514028 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \) |
${y}^2={x}^3+{x}^2-5{x}-5$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{6} \) |
$1.19516$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.275624609$ |
$2.141031885$ |
1.679514028 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 763\bigr] \) |
${y}^2={x}^3+{x}^2-165{x}+763$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.087062326 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.087062326 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.087062326 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.34418$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.087062326 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.899482172$ |
$6.875185818$ |
2.064855508 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.949741086$ |
$6.875185818$ |
2.064855508 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.798964345$ |
$6.875185818$ |
2.064855508 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-2{x}+3$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.34418$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.949741086$ |
$6.875185818$ |
2.064855508 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 3\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+3{x}+2$ |
| 40.1-a1 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{8} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.895399015 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 9\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+9{x}+5$ |
| 40.1-a2 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
1.895399015 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 4\) , \( 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+4{x}+4$ |
| 40.1-a3 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
1.895399015 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( -8\bigr] \) |
${y}^2={x}^3-8{x}-8$ |
| 40.1-a4 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.895399015 |
\( \frac{132304644}{5} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -21\) , \( 69\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-21{x}+69$ |
| 40.1-b1 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
0.947699507 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-b2 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
0.947699507 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \) |
${y}^2={x}^3-7{x}-6$ |
| 40.1-b3 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
0.947699507 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^3-2{x}+1$ |
| 40.1-b4 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2.996888981$ |
0.947699507 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) |
${y}^2={x}^3-107{x}-426$ |
| 44.1-a1 |
44.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{8} \cdot 11 \) |
$1.45557$ |
$(2,a), (a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$7.146887379$ |
0.753348076 |
\( -\frac{1372}{11} a + \frac{1372}{11} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -a - 2\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-a-2\right){x}+1$ |
| 44.1-a2 |
44.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{8} \cdot 11^{3} \) |
$1.45557$ |
$(2,a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.382295793$ |
0.753348076 |
\( -\frac{3109029596}{1331} a + \frac{9318326932}{1331} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a + 18\) , \( 4 a - 131\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(9a+18\right){x}+4a-131$ |
| 44.1-b1 |
44.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11 \) |
$1.45557$ |
$(2,a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$7.146887379$ |
2.260044229 |
\( -\frac{1372}{11} a + \frac{1372}{11} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( a + 2\bigr] \) |
${y}^2={x}^3+a{x}^2-{x}+a+2$ |
| 44.1-b2 |
44.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{3} \) |
$1.45557$ |
$(2,a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$2.382295793$ |
2.260044229 |
\( -\frac{3109029596}{1331} a + \frac{9318326932}{1331} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 40 a + 79\) , \( 9 a + 578\bigr] \) |
${y}^2={x}^3+a{x}^2+\left(40a+79\right){x}+9a+578$ |
| 44.2-a1 |
44.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{8} \cdot 11 \) |
$1.45557$ |
$(2,a), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$7.146887379$ |
0.753348076 |
\( \frac{1372}{11} a + \frac{1372}{11} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a-2\right){x}+1$ |
| 44.2-a2 |
44.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{8} \cdot 11^{3} \) |
$1.45557$ |
$(2,a), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2.382295793$ |
0.753348076 |
\( \frac{3109029596}{1331} a + \frac{9318326932}{1331} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -9 a + 18\) , \( -4 a - 131\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-9a+18\right){x}-4a-131$ |
| 44.2-b1 |
44.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11 \) |
$1.45557$ |
$(2,a), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$7.146887379$ |
2.260044229 |
\( \frac{1372}{11} a + \frac{1372}{11} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1\) , \( -a + 2\bigr] \) |
${y}^2={x}^3-a{x}^2-{x}-a+2$ |
| 44.2-b2 |
44.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{3} \) |
$1.45557$ |
$(2,a), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$2.382295793$ |
2.260044229 |
\( \frac{3109029596}{1331} a + \frac{9318326932}{1331} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 79\) , \( -9 a + 578\bigr] \) |
${y}^2={x}^3-a{x}^2+\left(-40a+79\right){x}-9a+578$ |
| 45.1-a1 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.537222968$ |
$0.558925428$ |
1.519247123 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 45.1-a2 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.148891872$ |
$8.942806850$ |
1.519247123 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 45.1-a3 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.297783744$ |
$1.117850856$ |
1.519247123 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 45.1-a4 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.148891872$ |
$2.235701712$ |
1.519247123 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 45.1-a5 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.297783744$ |
$4.471403425$ |
1.519247123 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 45.1-a6 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.074445936$ |
$1.117850856$ |
1.519247123 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 45.1-a7 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$8.595567489$ |
$2.235701712$ |
1.519247123 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 45.1-a8 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.148891872$ |
$0.558925428$ |
1.519247123 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 45.1-b1 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{32} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.558925428$ |
1.413981916 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -438\) , \( 7038\bigr] \) |
${y}^2+a{x}{y}={x}^3-438{x}+7038$ |
| 45.1-b2 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
1.413981916 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^3+2{x}-2$ |
| 45.1-b3 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{16} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
1.413981916 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 142\) , \( 222\bigr] \) |
${y}^2+a{x}{y}={x}^3+142{x}+222$ |
| 45.1-b4 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
1.413981916 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -38\) , \( 78\bigr] \) |
${y}^2+a{x}{y}={x}^3-38{x}+78$ |
| 45.1-b5 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
1.413981916 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -18\) , \( -18\bigr] \) |
${y}^2+a{x}{y}={x}^3-18{x}-18$ |
| 45.1-b6 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{4} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
1.413981916 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -538\) , \( 5278\bigr] \) |
${y}^2+a{x}{y}={x}^3-538{x}+5278$ |
| 45.1-b7 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2.235701712$ |
1.413981916 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -318\) , \( -1938\bigr] \) |
${y}^2+a{x}{y}={x}^3-318{x}-1938$ |
| 45.1-b8 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{2} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$0.558925428$ |
1.413981916 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -8638\) , \( 316318\bigr] \) |
${y}^2+a{x}{y}={x}^3-8638{x}+316318$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.49526$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 2\) , \( -2 a - 24\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-4a+2\right){x}-2a-24$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.49526$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( a + 7\) , \( -a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+7\right){x}-a+2$ |
*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.
