| 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 |
| 525.1-a1 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3 \cdot 5^{18} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.182944114$ |
1.437180430 |
\( -\frac{4163452939458406987237}{35888671875} a + \frac{11621395514320863711122}{35888671875} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -1073 a - 3918\) , \( -59174 a - 139962\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1073a-3918\right){x}-59174a-139962$ |
| 525.1-a2 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{3} \cdot 5^{6} \cdot 7^{12} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.646497027$ |
1.437180430 |
\( -\frac{1116422858941}{661775625} a + \frac{3869831168171}{661775625} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 152 a + 247\) , \( 1243 a + 2187\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(152a+247\right){x}+1243a+2187$ |
| 525.1-a3 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{6} \cdot 5^{6} \cdot 7^{6} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$6.585988108$ |
1.437180430 |
\( -\frac{1968209867}{1929375} a + \frac{894136682}{165375} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -43 a - 83\) , \( 82 a + 153\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-83\right){x}+82a+153$ |
| 525.1-a4 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{4} \cdot 5^{27} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$0.365888228$ |
1.437180430 |
\( \frac{3286347314559095552233}{3755092620849609375} a + \frac{942789826966264542718}{751018524169921875} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -1763 a - 3248\) , \( -47532 a - 85968\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1763a-3248\right){x}-47532a-85968$ |
| 525.1-a5 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{3} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.17197621$ |
1.437180430 |
\( -\frac{100272266627}{11025} a + \frac{11213978329}{441} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -18 a - 38\) , \( -103 a - 178\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a-38\right){x}-103a-178$ |
| 525.1-a6 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{12} \cdot 5^{9} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$3.292994054$ |
1.437180430 |
\( \frac{2903214315038687}{4651171875} a + \frac{3121066865015681}{2790703125} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -638 a - 1133\) , \( 12381 a + 22203\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-638a-1133\right){x}+12381a+22203$ |
| 525.1-a7 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{18} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.731776456$ |
1.437180430 |
\( \frac{8485224242586689}{5126953125} a + \frac{1262766196701523}{341796875} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -1618 a - 3023\) , \( -57143 a - 102873\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1618a-3023\right){x}-57143a-102873$ |
| 525.1-a8 |
525.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.463552913$ |
1.437180430 |
\( \frac{4948646226462039127}{328125} a + \frac{1772889969507804542}{65625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 1147 a - 3221\) , \( 9298 a - 25980\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1147a-3221\right){x}+9298a-25980$ |
| 525.1-b1 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{13} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$5.769014758$ |
$0.894985729$ |
3.380098590 |
\( \frac{1259048601200177}{35888671875} a - \frac{702888547069358}{7177734375} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 35 a - 92\) , \( 130 a - 394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(35a-92\right){x}+130a-394$ |
| 525.1-b2 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{7} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.923004919$ |
$8.054871564$ |
3.380098590 |
\( -\frac{6103957}{39375} a + \frac{3424171}{7875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 8\) , \( 4 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+8{x}+4a-4$ |
| 525.1-b3 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{4} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.769014758$ |
$0.447492864$ |
3.380098590 |
\( -\frac{2728519945338440457167911}{18375} a + \frac{4569650739014584468883452}{11025} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 8740 a - 24697\) , \( 673232 a - 1878956\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8740a-24697\right){x}+673232a-1878956$ |
| 525.1-b4 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{13} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.480751229$ |
$4.027435782$ |
3.380098590 |
\( -\frac{409618804330271}{107666015625} a + \frac{1442218014473851}{107666015625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 35 a - 127\) , \( -276 a + 656\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(35a-127\right){x}-276a+656$ |
| 525.1-b5 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{6} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.961502459$ |
$8.054871564$ |
3.380098590 |
\( \frac{2235488219}{328125} a + \frac{47198349574}{2953125} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a - 22\) , \( 6 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-22\right){x}+6a-16$ |
| 525.1-b6 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{6} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.884507379$ |
$0.894985729$ |
3.380098590 |
\( -\frac{30507583626037513}{5359375} a + \frac{7299077445885083}{459375} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 515 a - 1597\) , \( 9912 a - 28786\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(515a-1597\right){x}+9912a-28786$ |
| 525.1-b7 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{12} \cdot 5^{4} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.923004919$ |
$4.027435782$ |
3.380098590 |
\( \frac{18006302700317}{70875} a + \frac{295901264858807}{637875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 55 a - 397\) , \( 1076 a - 1916\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(55a-397\right){x}+1076a-1916$ |
| 525.1-b8 |
525.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{7} \cdot 7^{12} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.442253689$ |
$0.447492864$ |
3.380098590 |
\( \frac{342545846355593443}{220591875} a + \frac{613634004205251772}{220591875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -30 a - 2577\) , \( -2500 a - 50864\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a-2577\right){x}-2500a-50864$ |
| 525.1-c1 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{2} \cdot 5^{3} \cdot 7^{8} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.653725436$ |
$6.118976388$ |
3.491600165 |
\( -\frac{2398737609666907}{180075} a + \frac{6695567161558627}{180075} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 125 a + 194\) , \( 3909 a + 7065\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(125a+194\right){x}+3909a+7065$ |
| 525.1-c2 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{3} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.307450873$ |
$12.23795277$ |
3.491600165 |
\( -\frac{153721}{525} a + \frac{125998}{105} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -5 a + 14\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-5a+14\right){x}$ |
| 525.1-c3 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{6} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.653725436$ |
$12.23795277$ |
3.491600165 |
\( \frac{11927641}{13125} a + \frac{8818441}{2625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 20 a - 56\) , \( 5 a - 14\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(20a-56\right){x}+5a-14$ |
| 525.1-c4 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{6} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.326862718$ |
$12.23795277$ |
3.491600165 |
\( -\frac{14235870121}{275625} a + \frac{4755925414}{30625} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -100 a - 181\) , \( 594 a + 1065\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-100a-181\right){x}+594a+1065$ |
| 525.1-c5 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1.307450873$ |
$3.059488194$ |
3.491600165 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 225 a - 631\) , \( 2804 a - 7829\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(225a-631\right){x}+2804a-7829$ |
| 525.1-c6 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{8} \cdot 5^{9} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.163431359$ |
$6.118976388$ |
3.491600165 |
\( \frac{5191424415879943}{221484375} a + \frac{9299320211564417}{221484375} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 110 a - 321\) , \( -5045 a + 14101\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(110a-321\right){x}-5045a+14101$ |
| 525.1-d1 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{13} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$5.769014758$ |
$0.894985729$ |
3.380098590 |
\( -\frac{1259048601200177}{35888671875} a - \frac{2255394134146613}{35888671875} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 61\) , \( -224 a - 435\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-32a-61\right){x}-224a-435$ |
| 525.1-d2 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{7} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.923004919$ |
$8.054871564$ |
3.380098590 |
\( \frac{6103957}{39375} a + \frac{11016898}{39375} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 4\) , \( 2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+4\right){x}+2a+4$ |
| 525.1-d3 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{6} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.961502459$ |
$8.054871564$ |
3.380098590 |
\( -\frac{2235488219}{328125} a + \frac{13463548709}{590625} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -30 a - 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-21\right){x}-30a-31$ |
| 525.1-d4 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{13} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.480751229$ |
$4.027435782$ |
3.380098590 |
\( \frac{409618804330271}{107666015625} a + \frac{206519842028716}{21533203125} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 96\) , \( 147 a + 209\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-32a-96\right){x}+147a+209$ |
| 525.1-d5 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{7} \cdot 7^{12} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.442253689$ |
$0.447492864$ |
3.380098590 |
\( -\frac{342545846355593443}{220591875} a + \frac{191235970112169043}{44118375} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 33 a - 2611\) , \( -79 a - 53210\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-2611\right){x}-79a-53210$ |
| 525.1-d6 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{12} \cdot 5^{4} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.923004919$ |
$4.027435782$ |
3.380098590 |
\( -\frac{18006302700317}{70875} a + \frac{91591597832332}{127575} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -52 a - 346\) , \( -1475 a - 1111\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-52a-346\right){x}-1475a-1111$ |
| 525.1-d7 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{6} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.884507379$ |
$0.894985729$ |
3.380098590 |
\( \frac{30507583626037513}{5359375} a + \frac{163944959727865366}{16078125} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -512 a - 1086\) , \( -11511 a - 21445\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-512a-1086\right){x}-11511a-21445$ |
| 525.1-d8 |
525.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{4} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.769014758$ |
$0.447492864$ |
3.380098590 |
\( \frac{2728519945338440457167911}{18375} a + \frac{14662693859057600972913527}{55125} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -8737 a - 15961\) , \( -697931 a - 1249420\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8737a-15961\right){x}-697931a-1249420$ |
| 525.1-e1 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3 \cdot 5^{10} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.518830022$ |
$7.231173902$ |
1.637397992 |
\( -\frac{257906497658703295754}{8203125} a + \frac{143978254535512478441}{1640625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -509 a - 988\) , \( 12258 a + 22148\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-509a-988\right){x}+12258a+22148$ |
| 525.1-e2 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{8} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.259415011$ |
$3.615586951$ |
1.637397992 |
\( \frac{590589719}{972405} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -88 a + 244\) , \( -970 a + 2706\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-88a+244\right){x}-970a+2706$ |
| 525.1-e3 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{4} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.129707505$ |
$14.46234780$ |
1.637397992 |
\( \frac{47045881}{11025} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 37 a - 106\) , \( -125 a + 346\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(37a-106\right){x}-125a+346$ |
| 525.1-e4 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.259415011$ |
$14.46234780$ |
1.637397992 |
\( \frac{1771561}{105} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 12 a - 36\) , \( 42 a - 120\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-36\right){x}+42a-120$ |
| 525.1-e5 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.259415011$ |
$14.46234780$ |
1.637397992 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 562 a - 1576\) , \( -10688 a + 29830\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(562a-1576\right){x}-10688a+29830$ |
| 525.1-e6 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3 \cdot 5^{10} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.518830022$ |
$7.231173902$ |
1.637397992 |
\( \frac{257906497658703295754}{8203125} a + \frac{461984775018859096451}{8203125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 507 a - 1496\) , \( -12259 a + 34406\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(507a-1496\right){x}-12259a+34406$ |
| 525.1-f1 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{2} \cdot 5^{3} \cdot 7^{8} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.052007738$ |
1.836535274 |
\( -\frac{2398737609666907}{180075} a + \frac{6695567161558627}{180075} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 153 a - 410\) , \( 1627 a - 4685\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(153a-410\right){x}+1627a-4685$ |
| 525.1-f2 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{3} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$16.83212381$ |
1.836535274 |
\( -\frac{153721}{525} a + \frac{125998}{105} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 525.1-f3 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{6} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$16.83212381$ |
1.836535274 |
\( \frac{11927641}{13125} a + \frac{8818441}{2625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( -3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}-3$ |
| 525.1-f4 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{4} \cdot 5^{6} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.208030954$ |
1.836535274 |
\( -\frac{14235870121}{275625} a + \frac{4755925414}{30625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 35\) , \( 22 a - 110\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-35\right){x}+22a-110$ |
| 525.1-f5 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.83212381$ |
1.836535274 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 55\) , \( 22 a + 112\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-55\right){x}+22a+112$ |
| 525.1-f6 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{8} \cdot 5^{9} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.052007738$ |
1.836535274 |
\( \frac{5191424415879943}{221484375} a + \frac{9299320211564417}{221484375} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -67 a - 140\) , \( -475 a - 1083\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-67a-140\right){x}-475a-1083$ |
| 525.1-g1 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{4} \cdot 5^{27} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.636183209$ |
$0.996753031$ |
2.847081088 |
\( -\frac{3286347314559095552233}{3755092620849609375} a + \frac{2666765483130139421941}{1251697540283203125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -373 a - 1024\) , \( 19356 a + 36660\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-373a-1024\right){x}+19356a+36660$ |
| 525.1-g2 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{12} \cdot 5^{9} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.545394403$ |
$0.996753031$ |
2.847081088 |
\( -\frac{2903214315038687}{4651171875} a + \frac{24314977270194466}{13953515625} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 77 a + 11\) , \( -489 a - 1392\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(77a+11\right){x}-489a-1392$ |
| 525.1-g3 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.636183209$ |
$7.974024253$ |
2.847081088 |
\( -\frac{4948646226462039127}{328125} a + \frac{13813096074001061837}{328125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 22 a - 289\) , \( -486 a + 1515\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(22a-289\right){x}-486a+1515$ |
| 525.1-g4 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{6} \cdot 5^{6} \cdot 7^{6} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.272697201$ |
$3.987012126$ |
2.847081088 |
\( \frac{1968209867}{1929375} a + \frac{25390154269}{5788125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -28 a - 59\) , \( -146 a - 265\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-28a-59\right){x}-146a-265$ |
| 525.1-g5 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3^{3} \cdot 5^{6} \cdot 7^{12} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.545394403$ |
$1.993506063$ |
2.847081088 |
\( \frac{1116422858941}{661775625} a + \frac{550681661846}{132355125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -133 a - 209\) , \( 961 a + 1670\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-133a-209\right){x}+961a+1670$ |
| 525.1-g6 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{18} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.818091604$ |
$3.987012126$ |
2.847081088 |
\( -\frac{8485224242586689}{5126953125} a + \frac{27426717193109534}{5126953125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -553 a - 1319\) , \( 11803 a + 23528\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-553a-1319\right){x}+11803a+23528$ |
| 525.1-g7 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{3} \cdot 7^{3} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.545394403$ |
$7.974024253$ |
2.847081088 |
\( \frac{100272266627}{11025} a + \frac{180077191598}{11025} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -28 a - 54\) , \( -157 a - 277\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-28a-54\right){x}-157a-277$ |
| 525.1-g8 |
525.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( - 3 \cdot 5^{18} \cdot 7^{4} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.636183209$ |
$1.993506063$ |
2.847081088 |
\( \frac{4163452939458406987237}{35888671875} a + \frac{1491588514972491344777}{7177734375} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -9933 a - 18094\) , \( 814606 a + 1461968\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-9933a-18094\right){x}+814606a+1461968$ |
*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.
