| 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 |
| 225.1-a1 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{38} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.645391492$ |
2.253375518 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 334 a - 983\) , \( 9901 a - 27378\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(334a-983\right){x}+9901a-27378$ |
| 225.1-a2 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.32626388$ |
2.253375518 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4 a + 7\) , \( a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+7\right){x}+a+12$ |
| 225.1-a3 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.290782985$ |
2.253375518 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -101 a + 322\) , \( 547 a - 1437\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-101a+322\right){x}+547a-1437$ |
| 225.1-a4 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.163131942$ |
2.253375518 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 34 a - 83\) , \( 61 a - 168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a-83\right){x}+61a-168$ |
| 225.1-a5 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$10.32626388$ |
2.253375518 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 19 a - 38\) , \( -53 a + 153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-38\right){x}-53a+153$ |
| 225.1-a6 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.581565971$ |
2.253375518 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 409 a - 1208\) , \( 7111 a - 19743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(409a-1208\right){x}+7111a-19743$ |
| 225.1-a7 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.163131942$ |
2.253375518 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 244 a - 713\) , \( -3383 a + 9198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(244a-713\right){x}-3383a+9198$ |
| 225.1-a8 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.290782985$ |
2.253375518 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6484 a - 19433\) , \( 461521 a - 1272408\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6484a-19433\right){x}+461521a-1272408$ |
| 225.1-b1 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{38} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.645391492$ |
2.253375518 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -329 a - 657\) , \( -10557 a - 18475\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-329a-657\right){x}-10557a-18475$ |
| 225.1-b2 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.32626388$ |
2.253375518 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( a + 3\) , \( 3 a + 5\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+3\right){x}+3a+5$ |
| 225.1-b3 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.290782985$ |
2.253375518 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 106 a + 213\) , \( -333 a - 583\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(106a+213\right){x}-333a-583$ |
| 225.1-b4 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.163131942$ |
2.253375518 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -29 a - 57\) , \( -117 a - 205\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-29a-57\right){x}-117a-205$ |
| 225.1-b5 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$10.32626388$ |
2.253375518 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -14 a - 27\) , \( 27 a + 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-14a-27\right){x}+27a+47$ |
| 225.1-b6 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{22} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.581565971$ |
2.253375518 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -404 a - 807\) , \( -7917 a - 13855\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-404a-807\right){x}-7917a-13855$ |
| 225.1-b7 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.163131942$ |
2.253375518 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -239 a - 477\) , \( 2907 a + 5087\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-239a-477\right){x}+2907a+5087$ |
| 225.1-b8 |
225.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.290782985$ |
2.253375518 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -6479 a - 12957\) , \( -474477 a - 830335\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6479a-12957\right){x}-474477a-830335$ |
| 225.1-c1 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.036760681$ |
0.904958914 |
\( -\frac{359104782699}{244140625} a - \frac{52148361654}{48828125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -29 a + 6\) , \( -43 a - 145\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-29a+6\right){x}-43a-145$ |
| 225.1-c2 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$3.110282045$ |
0.904958914 |
\( \frac{359104782699}{244140625} a - \frac{619846590969}{244140625} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 285 a + 507\) , \( 1611 a + 2888\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(285a+507\right){x}+1611a+2888$ |
| 225.1-c3 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$12.44112818$ |
0.904958914 |
\( -\frac{118077162021}{15625} a + \frac{329617083726}{15625} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -75 a - 138\) , \( 72 a + 131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-75a-138\right){x}+72a+131$ |
| 225.1-c4 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$8.294085455$ |
0.904958914 |
\( -\frac{22825881}{125} a + \frac{12909294}{25} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a - 9\) , \( 2 a - 10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-9\right){x}+2a-10$ |
| 225.1-c5 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.220564091$ |
0.904958914 |
\( -\frac{32714515537919631}{125} a + \frac{91315629670496661}{125} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -675 a - 1263\) , \( -15543 a - 27694\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-675a-1263\right){x}-15543a-27694$ |
| 225.1-c6 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$24.88225636$ |
0.904958914 |
\( \frac{22825881}{125} a + \frac{41720589}{125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 23 a - 70\) , \( -60 a + 164\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23a-70\right){x}-60a+164$ |
| 225.1-c7 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$4.147042727$ |
0.904958914 |
\( \frac{118077162021}{15625} a + \frac{42307984341}{3125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 39\) , \( -52 a - 97\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a-39\right){x}-52a-97$ |
| 225.1-c8 |
225.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.073521363$ |
0.904958914 |
\( \frac{32714515537919631}{125} a + \frac{11720222826515406}{25} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -239 a - 564\) , \( -3697 a - 5977\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-239a-564\right){x}-3697a-5977$ |
| 225.1-d1 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$3.110282045$ |
0.904958914 |
\( -\frac{359104782699}{244140625} a - \frac{52148361654}{48828125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -287 a + 794\) , \( -1612 a + 4500\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-287a+794\right){x}-1612a+4500$ |
| 225.1-d2 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{16} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.036760681$ |
0.904958914 |
\( \frac{359104782699}{244140625} a - \frac{619846590969}{244140625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 28 a - 23\) , \( 42 a - 188\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(28a-23\right){x}+42a-188$ |
| 225.1-d3 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$4.147042727$ |
0.904958914 |
\( -\frac{118077162021}{15625} a + \frac{329617083726}{15625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 53\) , \( 51 a - 149\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-53\right){x}+51a-149$ |
| 225.1-d4 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$24.88225636$ |
0.904958914 |
\( -\frac{22825881}{125} a + \frac{12909294}{25} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -25 a - 46\) , \( 59 a + 105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-25a-46\right){x}+59a+105$ |
| 225.1-d5 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.073521363$ |
0.904958914 |
\( -\frac{32714515537919631}{125} a + \frac{91315629670496661}{125} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 238 a - 803\) , \( 3696 a - 9674\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(238a-803\right){x}+3696a-9674$ |
| 225.1-d6 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$8.294085455$ |
0.904958914 |
\( \frac{22825881}{125} a + \frac{41720589}{125} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a - 8\) , \( -3 a - 8\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-8\right){x}-3a-8$ |
| 225.1-d7 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$12.44112818$ |
0.904958914 |
\( \frac{118077162021}{15625} a + \frac{42307984341}{3125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 73 a - 211\) , \( -73 a + 204\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(73a-211\right){x}-73a+204$ |
| 225.1-d8 |
225.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.58597$ |
$(-a+2), (-a), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$6.220564091$ |
0.904958914 |
\( \frac{32714515537919631}{125} a + \frac{11720222826515406}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 673 a - 1936\) , \( 15542 a - 43236\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(673a-1936\right){x}+15542a-43236$ |
*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.
