| 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 |
| 300.1-a1 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.634533048 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 300.1-a2 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.634533048 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 300.1-a3 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.634533048 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 300.1-a4 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.808889283$ |
1.634533048 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 300.1-a5 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.634533048 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
| 300.1-a6 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.634533048 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 300.1-a7 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.634533048 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 300.1-a8 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.312098809$ |
1.634533048 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
| 300.1-b1 |
300.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.341399975$ |
2.043741451 |
\( -\frac{23869147}{324} a - \frac{71336321}{540} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 3 a - 11\) , \( 22 a - 64\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(3a-11\right){x}+22a-64$ |
| 300.1-b2 |
300.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.341399975$ |
2.043741451 |
\( \frac{2250110140541}{90} a + \frac{10076573441941}{225} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 93 a - 281\) , \( 796 a - 2260\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(93a-281\right){x}+796a-2260$ |
| 300.1-c1 |
300.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.341399975$ |
2.043741451 |
\( \frac{23869147}{324} a - \frac{166677349}{810} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -4 a - 8\) , \( -23 a - 42\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a-8\right){x}-23a-42$ |
| 300.1-c2 |
300.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.341399975$ |
2.043741451 |
\( -\frac{2250110140541}{90} a + \frac{3489299731843}{50} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -94 a - 188\) , \( -797 a - 1464\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-94a-188\right){x}-797a-1464$ |
| 300.1-d1 |
300.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{16} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.120031321$ |
$2.588605064$ |
1.898491981 |
\( -\frac{119817845337407}{109863281250} a - \frac{4662657100983}{2441406250} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -15 a - 6\) , \( 69 a - 108\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-15a-6\right){x}+69a-108$ |
| 300.1-d2 |
300.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.060015660$ |
$10.35442025$ |
1.898491981 |
\( \frac{6559560353773}{937500} a + \frac{1176618663029}{93750} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -5 a - 36\) , \( 23 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-36\right){x}+23a+6$ |
| 300.1-e1 |
300.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{16} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.120031321$ |
$2.588605064$ |
1.898491981 |
\( \frac{119817845337407}{109863281250} a - \frac{164818707440821}{54931640625} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 16 a - 18\) , \( -74 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(16a-18\right){x}-74a+38$ |
| 300.1-e2 |
300.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.060015660$ |
$10.35442025$ |
1.898491981 |
\( -\frac{6559560353773}{937500} a + \frac{6108582328021}{312500} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 6 a - 38\) , \( -58 a + 56\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a-38\right){x}-58a+56$ |
| 300.1-f1 |
300.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{16} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.453942994$ |
1.269105490 |
\( \frac{119817845337407}{109863281250} a - \frac{164818707440821}{54931640625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 101 a + 179\) , \( 5163 a + 9246\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(101a+179\right){x}+5163a+9246$ |
| 300.1-f2 |
300.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.815771977$ |
1.269105490 |
\( -\frac{6559560353773}{937500} a + \frac{6108582328021}{312500} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -139 a - 251\) , \( 1359 a + 2432\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-139a-251\right){x}+1359a+2432$ |
| 300.1-g1 |
300.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{16} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.453942994$ |
1.269105490 |
\( -\frac{119817845337407}{109863281250} a - \frac{4662657100983}{2441406250} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -101 a + 285\) , \( -5265 a + 14695\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-101a+285\right){x}-5265a+14695$ |
| 300.1-g2 |
300.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.815771977$ |
1.269105490 |
\( \frac{6559560353773}{937500} a + \frac{1176618663029}{93750} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 139 a - 385\) , \( -1221 a + 3407\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(139a-385\right){x}-1221a+3407$ |
| 300.1-h1 |
300.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.263908879$ |
$19.41067282$ |
2.235707275 |
\( \frac{23869147}{324} a - \frac{166677349}{810} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 6 a - 16\) , \( -9 a + 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(6a-16\right){x}-9a+26$ |
| 300.1-h2 |
300.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.131954439$ |
$19.41067282$ |
2.235707275 |
\( -\frac{2250110140541}{90} a + \frac{3489299731843}{50} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 96 a - 286\) , \( -765 a + 2150\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(96a-286\right){x}-765a+2150$ |
| 300.1-i1 |
300.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.263908879$ |
$19.41067282$ |
2.235707275 |
\( -\frac{23869147}{324} a - \frac{71336321}{540} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -7 a - 10\) , \( 9 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-10\right){x}+9a+17$ |
| 300.1-i2 |
300.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.131954439$ |
$19.41067282$ |
2.235707275 |
\( \frac{2250110140541}{90} a + \frac{10076573441941}{225} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -97 a - 190\) , \( 765 a + 1385\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-97a-190\right){x}+765a+1385$ |
| 300.1-j1 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.722815623$ |
$5.367489134$ |
2.539863122 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 67 a - 190\) , \( -1463 a + 4081\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(67a-190\right){x}-1463a+4081$ |
| 300.1-j2 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.168446869$ |
$5.367489134$ |
2.539863122 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -8 a + 20\) , \( 46 a - 131\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-8a+20\right){x}+46a-131$ |
| 300.1-j3 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
$0.180703905$ |
$1.341872283$ |
2.539863122 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -2269 a - 4082\) , \( 10782 a + 19299\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2269a-4082\right){x}+10782a+19299$ |
| 300.1-j4 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.168446869$ |
$5.367489134$ |
2.539863122 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 342 a - 960\) , \( -4308 a + 12021\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(342a-960\right){x}-4308a+12021$ |
| 300.1-j5 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1.084223434$ |
$5.367489134$ |
2.539863122 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 92 a - 260\) , \( 722 a - 2019\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(92a-260\right){x}+722a-2019$ |
| 300.1-j6 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$0.361407811$ |
$5.367489134$ |
2.539863122 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 1667 a - 4670\) , \( -55159 a + 153969\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1667a-4670\right){x}-55159a+153969$ |
| 300.1-j7 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$0.542111717$ |
$1.341872283$ |
2.539863122 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 1442 a - 4040\) , \( 46136 a - 128811\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1442a-4040\right){x}+46136a-128811$ |
| 300.1-j8 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.722815623$ |
$5.367489134$ |
2.539863122 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 26667 a - 74670\) , \( -3582159 a + 9999969\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(26667a-74670\right){x}-3582159a+9999969$ |
*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.
