| 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 |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.81899$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 7$ |
2B, 7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-2$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.81899$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 7$ |
2B, 7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}$ |
| 25.2-b1 |
25.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$0.91566$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.139669982$ |
$16.42661250$ |
1.001316654 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 2\) , \( -2 a + 4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-2a+4$ |
| 25.2-b2 |
25.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$0.91566$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.046556660$ |
$16.42661250$ |
1.001316654 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 2\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-a-2$ |
| 25.3-b1 |
25.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{4} \) |
$0.91566$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.139669982$ |
$16.42661250$ |
1.001316654 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+a+1$ |
| 25.3-b2 |
25.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{4} \) |
$0.91566$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.046556660$ |
$16.42661250$ |
1.001316654 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}$ |
| 49.1-a1 |
49.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{8} \) |
$1.08342$ |
$(a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7.676076964$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( 5 a - 16\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+5a-16$ |
| 49.1-a2 |
49.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{8} \) |
$1.08342$ |
$(a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.2 |
$1$ |
\( 1 \) |
$1$ |
$7.676076964$ |
1.675057320 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( -5 a - 9\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-5a-9$ |
| 81.1-a3 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$1.22848$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3Cs, 7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$9.363037422$ |
2.043182272 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 3 a + 5\bigr] \) |
${y}^2+{y}={x}^{3}+3a+5$ |
| 81.1-a4 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$1.22848$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3Cs, 7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$9.363037422$ |
2.043182272 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -3 a + 8\bigr] \) |
${y}^2+{y}={x}^{3}-3a+8$ |
| 81.1-b3 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$1.22848$ |
$(-a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3Cs.1.1, 7Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$28.08911226$ |
0.681060757 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 81.1-b4 |
81.1-b |
$4$ |
$27$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$1.22848$ |
$(-a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3Cs.1.1, 7Ns.3.1 |
$1$ |
\( 3 \) |
$1$ |
$9.363037422$ |
0.681060757 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 6 a - 17\bigr] \) |
${y}^2+{y}={x}^{3}+6a-17$ |
| 144.1-a1 |
144.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.41853$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3, 7$ |
2B, 3B.1.2, 7Ns.3.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.526895372$ |
$5.898343969$ |
2.034539317 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -24 a - 43\bigr] \) |
${y}^2={x}^{3}-24a-43$ |
| 144.1-a2 |
144.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.41853$ |
$(-a+2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3, 7$ |
2B, 3B.1.1, 7Ns.3.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.580686117$ |
$17.69503190$ |
2.034539317 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^{3}+1$ |
| 225.2-b1 |
225.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.2, 7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$5.475537501$ |
2.389720482 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-4$ |
| 225.2-b2 |
225.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1, 7Ns.3.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$16.42661250$ |
2.389720482 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 9 a + 16\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+9a+16$ |
| 225.3-b1 |
225.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.2, 7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$5.475537501$ |
2.389720482 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -a - 3\bigr] \) |
${y}^2+a{y}={x}^{3}-a-3$ |
| 225.3-b2 |
225.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1, 7Ns.3.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$16.42661250$ |
2.389720482 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -10 a + 26\bigr] \) |
${y}^2+a{y}={x}^{3}-10a+26$ |
| 256.1-d1 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.63798$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 7$ |
2B, 7Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}$ |
| 256.1-d2 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.63798$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 7$ |
2B, 7Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.965343132 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+2$ |
| 400.2-a1 |
400.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{8} \) |
$1.83132$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1.743375040$ |
$3.812279058$ |
2.900653519 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( -8 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-8a+3$ |
| 400.2-a2 |
400.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{8} \) |
$1.83132$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.581125013$ |
$3.812279058$ |
2.900653519 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 416 a - 1163\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+416a-1163$ |
| 400.3-a1 |
400.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{8} \) |
$1.83132$ |
$(-a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1.743375040$ |
$3.812279058$ |
2.900653519 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 8 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+8a-7$ |
| 400.3-a2 |
400.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{8} \) |
$1.83132$ |
$(-a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.581125013$ |
$3.812279058$ |
2.900653519 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( -416 a - 745\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-416a-745$ |
| 441.1-d1 |
441.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$1.87654$ |
$(-a+2), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3B.1.2, 7Cs.6.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.298091926$ |
$2.558692321$ |
1.997284256 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -294 a - 527\bigr] \) |
${y}^2+{y}={x}^{3}-294a-527$ |
| 441.1-d2 |
441.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$1.87654$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3B.1.1, 7Cs.6.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.894275780$ |
$7.676076964$ |
1.997284256 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 12\bigr] \) |
${y}^2+{y}={x}^{3}+12$ |
| 625.1-c1 |
625.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{4} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Ns.2.1, 7Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$16.42661250$ |
3.584580724 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( -a - 2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-a-2$ |
| 625.1-c2 |
625.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{4} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Ns.2.1, 7Ns.3.1 |
$1$ |
\( 1 \) |
$1$ |
$16.42661250$ |
3.584580724 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( a - 1\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+a-1$ |
| 625.1-j1 |
625.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.285322500$ |
1.433832289 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 2\) , \( -213 a + 588\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-213a+588$ |
| 625.1-j2 |
625.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.285322500$ |
1.433832289 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 2\) , \( 24 a + 34\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+24a+34$ |
| 625.1-p1 |
625.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Ns.2.1, 7Ns.2.1 |
$1$ |
\( 3 \) |
$1$ |
$3.285322500$ |
2.150748434 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( 69 a - 192\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+69a-192$ |
| 625.1-p2 |
625.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5, 7$ |
5Ns.2.1, 7Ns.2.1 |
$1$ |
\( 3 \) |
$1$ |
$3.285322500$ |
2.150748434 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( -69 a - 121\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-69a-121$ |
| 625.1-q1 |
625.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.285322500$ |
1.433832289 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( -25 a + 57\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-25a+57$ |
| 625.1-q2 |
625.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{16} \) |
$2.04747$ |
$(-a), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 2 \) |
$1$ |
$3.285322500$ |
1.433832289 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( 212 a + 378\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+212a+378$ |
| 729.1-a1 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{12} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.690454106$ |
$9.363037422$ |
2.821447178 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -15 a - 27\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-15a-27$ |
| 729.1-a2 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{12} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.230151368$ |
$9.363037422$ |
2.821447178 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-3$ |
| 729.1-b1 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{12} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$0.690454106$ |
$9.363037422$ |
2.821447178 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 14 a - 41\bigr] \) |
${y}^2+a{y}={x}^{3}+14a-41$ |
| 729.1-b2 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{12} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.230151368$ |
$9.363037422$ |
2.821447178 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -a - 2\bigr] \) |
${y}^2+a{y}={x}^{3}-a-2$ |
| 729.1-c1 |
729.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.2, 7Ns.3.1 |
$1$ |
\( 1 \) |
$0.977127928$ |
$9.363037422$ |
3.992900922 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}-2$ |
| 729.1-c2 |
729.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1, 7Ns.3.1 |
$1$ |
\( 1 \) |
$2.931383785$ |
$28.08911226$ |
3.992900922 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+a+1$ |
| 729.1-d1 |
729.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.2, 7Ns.3.1 |
$1$ |
\( 1 \) |
$0.977127928$ |
$9.363037422$ |
3.992900922 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a-2$ |
| 729.1-d2 |
729.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$2.12780$ |
$(-a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1, 7Ns.3.1 |
$1$ |
\( 1 \) |
$2.931383785$ |
$28.08911226$ |
3.992900922 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -2 a + 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-2a+2$ |
| 784.1-e1 |
784.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.16684$ |
$(a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$5.827272664$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 12 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+12a+21$ |
| 784.1-e2 |
784.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{4} \) |
$2.16684$ |
$(a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$5.827272664$ |
1.271615146 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( -12 a + 35\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-12a+35$ |
| 1225.2-a1 |
1225.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{8} \cdot 7^{4} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 1 \) |
$1.248524248$ |
$5.021791350$ |
2.736377394 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( -182 a + 508\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-182a+508$ |
| 1225.2-a2 |
1225.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{8} \cdot 7^{4} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.2.1 |
$1$ |
\( 3 \) |
$0.416174749$ |
$5.021791350$ |
2.736377394 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( 3 a - 3\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+3a-3$ |
| 1225.2-b1 |
1225.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{2} \cdot 7^{10} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 1 \) |
$1.382361320$ |
$7.351149817$ |
4.435036470 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( 17 a + 32\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+17a+32$ |
| 1225.2-b2 |
1225.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{2} \cdot 7^{10} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Ns.3.1 |
$1$ |
\( 1 \) |
$4.147083961$ |
$2.450383272$ |
4.435036470 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( 56 a - 157\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+56a-157$ |
| 1225.2-c1 |
1225.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{2} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Cs.6.2 |
$1$ |
\( 2 \) |
$0.156143787$ |
$15.73127654$ |
2.144070295 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( -18 a + 48\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-18a+48$ |
| 1225.2-c2 |
1225.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1225.2 |
\( 5^{2} \cdot 7^{2} \) |
\( 5^{6} \cdot 7^{2} \) |
$2.42260$ |
$(-a), (a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$7$ |
7Cs.6.2 |
$1$ |
\( 2 \) |
$0.468431363$ |
$5.243758848$ |
2.144070295 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-1$ |
*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.
