| 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 |
| 900.1-a1 |
900.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.122875313$ |
0.866129774 |
\( -\frac{3869893}{300} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 11 a - 21\) , \( 28 a - 63\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(11a-21\right){x}+28a-63$ |
| 900.1-a2 |
900.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.122875313$ |
0.866129774 |
\( \frac{16718302693}{90} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -160 a - 214\) , \( -1388 a - 1814\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-160a-214\right){x}-1388a-1814$ |
| 900.1-b1 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.248395236$ |
3.116182873 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 900.1-b2 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$11.23555713$ |
3.116182873 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 900.1-b3 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.248395236$ |
3.116182873 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 900.1-b4 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$2.808889283$ |
3.116182873 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 900.1-b5 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$11.23555713$ |
3.116182873 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
| 900.1-b6 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.248395236$ |
3.116182873 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 900.1-b7 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$11.23555713$ |
3.116182873 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 900.1-b8 |
900.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.312098809$ |
3.116182873 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
| 900.1-c1 |
900.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( \frac{1847535679891}{21870000} a - \frac{4238649701599}{21870000} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 28 a + 4\) , \( -102 a - 67\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a+4\right){x}-102a-67$ |
| 900.1-c2 |
900.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( -\frac{12308796013854397057}{478296900} a + \frac{7086099344364355471}{119574225} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 28 a - 496\) , \( -1902 a + 2133\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a-496\right){x}-1902a+2133$ |
| 900.1-c3 |
900.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( -\frac{52222361160990251070049771}{21870} a + \frac{120256381026369874209043399}{21870} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 1678 a - 6346\) , \( -70482 a + 209493\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1678a-6346\right){x}-70482a+209493$ |
| 900.1-c4 |
900.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.066460414$ |
1.183131602 |
\( \frac{522448577782306226513}{228767924549610} a + \frac{750488738989577522683}{228767924549610} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -1622 a - 2646\) , \( -54522 a - 66427\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1622a-2646\right){x}-54522a-66427$ |
| 900.1-d1 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( -\frac{1847535679891}{21870000} a - \frac{199259501809}{1822500} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -28 a + 32\) , \( 74 a - 137\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-28a+32\right){x}+74a-137$ |
| 900.1-d2 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{32} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.066460414$ |
1.183131602 |
\( -\frac{522448577782306226513}{228767924549610} a + \frac{212156219461980624866}{38127987424935} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1622 a - 4268\) , \( 56144 a - 125217\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1622a-4268\right){x}+56144a-125217$ |
| 900.1-d3 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( \frac{12308796013854397057}{478296900} a + \frac{5345200454534341609}{159432300} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -28 a - 468\) , \( 1874 a - 237\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-28a-468\right){x}+1874a-237$ |
| 900.1-d4 |
900.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$4.265841659$ |
1.183131602 |
\( \frac{52222361160990251070049771}{21870} a + \frac{11339003310896603856498938}{3645} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -1678 a - 4668\) , \( 68804 a + 134343\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1678a-4668\right){x}+68804a+134343$ |
| 900.1-e1 |
900.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.084370331$ |
$4.641181765$ |
2.606501006 |
\( -\frac{13244532371}{26572050} a + \frac{13475569282}{13286025} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -24 a + 56\) , \( 26 a - 58\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-24a+56\right){x}+26a-58$ |
| 900.1-e2 |
900.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.042185165$ |
$18.56472706$ |
2.606501006 |
\( \frac{1491708701}{14580} a + \frac{1969525423}{14580} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a - 14\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6a-14\right){x}$ |
| 900.1-f1 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{40} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.352451450$ |
0.782019554 |
\( -\frac{29273545574291579380528499}{30018927059399824200} a - \frac{9534328730560649185054291}{7504731764849956050} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -14836 a - 19566\) , \( 1327874 a + 1714566\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14836a-19566\right){x}+1327874a+1714566$ |
| 900.1-f2 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{40} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.352451450$ |
0.782019554 |
\( \frac{29273545574291579380528499}{30018927059399824200} a - \frac{22470286832178058706915221}{10006309019799941400} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 14835 a - 34401\) , \( -1327875 a + 3042441\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(14835a-34401\right){x}-1327875a+3042441$ |
| 900.1-f3 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{24} \cdot 5^{12} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$0.352451450$ |
0.782019554 |
\( \frac{63745936931123}{4251528000000} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -2496 a + 5827\) , \( -987041 a + 2275772\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2496a+5827\right){x}-987041a+2275772$ |
| 900.1-f4 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{12} \cdot 5^{6} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.409805800$ |
0.782019554 |
\( \frac{570403428460237}{23887872000} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5184 a - 12093\) , \( -264097 a + 608700\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(5184a-12093\right){x}-264097a+608700$ |
| 900.1-f5 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.409805800$ |
0.782019554 |
\( -\frac{425257563110754496222541}{123974556480} a + \frac{81606064373112754957537}{10331213040} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 14715 a - 34561\) , \( -1325363 a + 3045025\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(14715a-34561\right){x}-1325363a+3045025$ |
| 900.1-f6 |
900.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.409805800$ |
0.782019554 |
\( \frac{425257563110754496222541}{123974556480} a + \frac{554015209366598563267903}{123974556480} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -14716 a - 19846\) , \( 1325362 a + 1719662\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14716a-19846\right){x}+1325362a+1719662$ |
| 900.1-g1 |
900.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.084370331$ |
$4.641181765$ |
2.606501006 |
\( \frac{13244532371}{26572050} a + \frac{4568868731}{8857350} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 24 a + 32\) , \( -26 a - 32\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(24a+32\right){x}-26a-32$ |
| 900.1-g2 |
900.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.042185165$ |
$18.56472706$ |
2.606501006 |
\( -\frac{1491708701}{14580} a + \frac{288436177}{1215} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a - 8\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-8\right){x}$ |
| 900.1-h1 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{20} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.496206767$ |
$0.136787812$ |
3.030443996 |
\( -\frac{44410745345557732394514941}{2152336050} a + \frac{51133991217633370516994401}{1076168025} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 6390 a - 16440\) , \( 400050 a - 963450\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6390a-16440\right){x}+400050a-963450$ |
| 900.1-h2 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{34} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.248103383$ |
$0.547151249$ |
3.030443996 |
\( \frac{9392714743674271079}{37060403777036820} a + \frac{4613417879226797543}{12353467925678940} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 90 a + 190\) , \( -240 a - 1812\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(90a+190\right){x}-240a-1812$ |
| 900.1-h3 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.624051691$ |
$2.188604997$ |
3.030443996 |
\( -\frac{68275978021097}{17218688400} a + \frac{17370123113857}{1434890700} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 110\) , \( -60 a - 372\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-110\right){x}-60a-372$ |
| 900.1-h4 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{10} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.312025845$ |
$8.754419991$ |
3.030443996 |
\( \frac{61245601549}{8398080} a + \frac{38348044213}{2799360} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 30\) , \( 20 a + 60\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-30\right){x}+20a+60$ |
| 900.1-h5 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{8} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.248103383$ |
$0.547151249$ |
3.030443996 |
\( -\frac{406708983572281}{5467500} a + \frac{2884346145937087}{16402500} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -110 a - 1690\) , \( -3400 a - 26900\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-110a-1690\right){x}-3400a-26900$ |
| 900.1-h6 |
900.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{8} \cdot 5^{16} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.496206767$ |
$0.136787812$ |
3.030443996 |
\( \frac{363584079429415348789}{63281250} a + \frac{236834239974538749911}{31640625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -8210 a - 12220\) , \( -587410 a - 788462\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8210a-12220\right){x}-587410a-788462$ |
| 900.1-i1 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{8} \cdot 5^{16} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.496206767$ |
$0.136787812$ |
3.030443996 |
\( -\frac{363584079429415348789}{63281250} a + \frac{837252559378492848611}{63281250} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 8212 a - 20429\) , \( 575190 a - 1351240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(8212a-20429\right){x}+575190a-1351240$ |
| 900.1-i2 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{34} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.248103383$ |
$0.547151249$ |
3.030443996 |
\( -\frac{9392714743674271079}{37060403777036820} a + \frac{5808242095338665927}{9265100944259205} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -88 a + 281\) , \( 430 a - 2320\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-88a+281\right){x}+430a-2320$ |
| 900.1-i3 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{10} \cdot 5^{2} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.312025845$ |
$8.754419991$ |
3.030443996 |
\( -\frac{61245601549}{8398080} a + \frac{44072433547}{2099520} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 12 a - 39\) , \( -50 a + 112\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(12a-39\right){x}-50a+112$ |
| 900.1-i4 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.624051691$ |
$2.188604997$ |
3.030443996 |
\( \frac{68275978021097}{17218688400} a + \frac{140165499345187}{17218688400} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 12 a - 119\) , \( -50 a - 400\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(12a-119\right){x}-50a-400$ |
| 900.1-i5 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 5^{8} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.248103383$ |
$0.547151249$ |
3.030443996 |
\( \frac{406708983572281}{5467500} a + \frac{416054798805061}{4100625} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 112 a - 1799\) , \( 1710 a - 29968\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(112a-1799\right){x}+1710a-29968$ |
| 900.1-i6 |
900.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{20} \cdot 5^{4} \) |
$1.76470$ |
$(-a), (-a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.496206767$ |
$0.136787812$ |
3.030443996 |
\( \frac{44410745345557732394514941}{2152336050} a + \frac{19285745696569669546491287}{717445350} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -6388 a - 10049\) , \( -416490 a - 582568\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6388a-10049\right){x}-416490a-582568$ |
*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.
