| 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 |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$0.79925$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.594800260$ |
0.960927881 |
\( 2048 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \) |
${y}^2={x}^3-a{x}^2+{x}-a$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.79925$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.594800260$ |
0.960927881 |
\( 78608 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -a + 3\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-a+3\right){x}+1$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$0.79925$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.594800260$ |
0.960927881 |
\( 2048 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( a\bigr] \) |
${y}^2={x}^3+a{x}^2+{x}+a$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.79925$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.594800260$ |
0.960927881 |
\( 78608 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -a + 3\) , \( -a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-a+3\right){x}-a+1$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2.141031885$ |
0.478749283 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
0.478749283 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) |
${y}^2={x}^3+{x}^2+4{x}+4$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.423095656$ |
0.478749283 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-{x}$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2.141031885$ |
0.478749283 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-116$ |
| 20.1-b1 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.141031885$ |
1.436247851 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^3-{x}^2-36{x}+140$ |
| 20.1-b2 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.423095656$ |
1.436247851 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \) |
${y}^2={x}^3-{x}^2+4{x}-4$ |
| 20.1-b3 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.423095656$ |
1.436247851 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2-{x}$ |
| 20.1-b4 |
20.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$0.84511$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.141031885$ |
1.436247851 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^3-{x}^2-41{x}+116$ |
| 40.1-a1 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.233348375$ |
$2.996888981$ |
1.250980172 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-a2 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.466696751$ |
$5.993777963$ |
1.250980172 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \) |
${y}^2={x}^3-7{x}-6$ |
| 40.1-a3 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.933393502$ |
$5.993777963$ |
1.250980172 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^3-2{x}+1$ |
| 40.1-a4 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.933393502$ |
$2.996888981$ |
1.250980172 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) |
${y}^2={x}^3-107{x}-426$ |
| 40.1-b1 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
1.340249496 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \) |
${y}^2={x}^3+13{x}+34$ |
| 40.1-b2 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-b3 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
1.340249496 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2={x}^3-2{x}-1$ |
| 40.1-b4 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$2.996888981$ |
1.340249496 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \) |
${y}^2={x}^3-107{x}+426$ |
| 45.2-a1 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{40} \cdot 5 \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.279462714$ |
0.499918100 |
\( -\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -395 a + 90\) , \( 2916 a - 8170\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+\left(-395a+90\right){x}+2916a-8170$ |
| 45.2-a2 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{40} \cdot 5 \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.279462714$ |
0.499918100 |
\( \frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 395 a + 90\) , \( -2916 a - 8170\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+\left(395a+90\right){x}-2916a-8170$ |
| 45.2-a3 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$0.558925428$ |
0.499918100 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 45.2-a4 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
0.499918100 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 45.2-a5 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.117850856$ |
0.499918100 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 45.2-a6 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.235701712$ |
0.499918100 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 45.2-a7 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
0.499918100 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 45.2-a8 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.499918100 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 45.2-a9 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.499918100 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 45.2-a10 |
45.2-a |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$0.558925428$ |
0.499918100 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 45.2-b1 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{40} \cdot 5 \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.279462714$ |
1.999672402 |
\( -\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -395 a + 93\) , \( -2916 a + 8171\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-395a+93\right){x}-2916a+8171$ |
| 45.2-b2 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{40} \cdot 5 \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.279462714$ |
1.999672402 |
\( \frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 395 a + 93\) , \( 2916 a + 8171\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(395a+93\right){x}+2916a+8171$ |
| 45.2-b3 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.558925428$ |
1.999672402 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -107\) , \( 881\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-107{x}+881$ |
| 45.2-b4 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
1.999672402 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+3{x}+1$ |
| 45.2-b5 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.117850856$ |
1.999672402 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 38\) , \( 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+38{x}+29$ |
| 45.2-b6 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$2.235701712$ |
1.999672402 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-7{x}+11$ |
| 45.2-b7 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
1.999672402 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-2{x}-1$ |
| 45.2-b8 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$1.117850856$ |
1.999672402 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -132\) , \( 661\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-132{x}+661$ |
| 45.2-b9 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2.235701712$ |
1.999672402 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -77\) , \( -241\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-77{x}-241$ |
| 45.2-b10 |
45.2-b |
$10$ |
$32$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$1.03504$ |
$(3,a+1), (3,a+2), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.558925428$ |
1.999672402 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2157\) , \( 39541\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-2157{x}+39541$ |
| 50.1-a1 |
50.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{8} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \) |
$1$ |
$1.424166746$ |
1.273813462 |
\( -\frac{349938025}{8} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-126{x}-552$ |
| 50.1-a2 |
50.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.272500240$ |
1.273813462 |
\( -\frac{121945}{32} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3$ |
| 50.1-a3 |
50.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.272500240$ |
1.273813462 |
\( -\frac{25}{2} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}-2$ |
| 50.1-a4 |
50.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.3 |
$1$ |
\( 2 \) |
$1$ |
$1.424166746$ |
1.273813462 |
\( \frac{46969655}{32768} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 25\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+25{x}+10$ |
| 50.1-b1 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{8} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.194697629$ |
$1.424166746$ |
1.488050770 |
\( -\frac{349938025}{8} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -123\) , \( 553\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-123{x}+553$ |
| 50.1-b2 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.324496049$ |
$4.272500240$ |
1.488050770 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-3{x}+1$ |
| 50.1-b3 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{8} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.064899209$ |
$4.272500240$ |
1.488050770 |
\( -\frac{25}{2} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+2{x}+3$ |
| 50.1-b4 |
50.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
50.1 |
\( 2 \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.06266$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.973488147$ |
$1.424166746$ |
1.488050770 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+22{x}-9$ |
| 64.1-a1 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$1.13031$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 5$ |
2Cs, 5Ns.2.1 |
$1$ |
\( 2 \) |
$1.899482172$ |
$6.875185818$ |
1.460073332 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 64.1-a2 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{24} \) |
$1.13031$ |
$(2,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 5$ |
2Cs, 5Ns.2.1 |
$1$ |
\( 2^{2} \) |
$0.949741086$ |
$6.875185818$ |
1.460073332 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
*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.
