| 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 |
| 45.1-a1 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{10} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$0.156385680$ |
$7827.540648$ |
3.29637 |
\( -\frac{4702123576857616}{9375} a^{5} + \frac{722454184206072}{3125} a^{4} + \frac{6383172803344204}{1875} a^{3} - \frac{5306831170078837}{9375} a^{2} - \frac{49277299547829394}{9375} a - \frac{27203459111363}{25} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -3 a^{5} + a^{4} + 21 a^{3} - a^{2} - 34 a - 9\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( -54 a^{5} + 50 a^{4} + 320 a^{3} - 170 a^{2} - 377 a - 100\) , \( 194 a^{5} - 228 a^{4} - 1073 a^{3} + 851 a^{2} + 1049 a + 215\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}-a^{2}-34a-9\right){x}^{2}+\left(-54a^{5}+50a^{4}+320a^{3}-170a^{2}-377a-100\right){x}+194a^{5}-228a^{4}-1073a^{3}+851a^{2}+1049a+215$ |
| 45.1-a2 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{20} \cdot 5^{4} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.062554272$ |
$1956.885162$ |
3.29637 |
\( \frac{132995277174727124}{1476225} a^{5} + \frac{299238637140317522}{1476225} a^{4} - \frac{257681353571429176}{1476225} a^{3} - \frac{845771537745059027}{1476225} a^{2} - \frac{440033964830611637}{1476225} a - \frac{59108871769893511}{1476225} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( a^{3} - 4 a - 2\) , \( a + 1\) , \( 11 a^{5} - a^{4} - 54 a^{3} - 21 a^{2} + 43 a + 20\) , \( -a^{5} + 31 a^{4} - 105 a^{2} - 82 a - 17\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(11a^{5}-a^{4}-54a^{3}-21a^{2}+43a+20\right){x}-a^{5}+31a^{4}-105a^{2}-82a-17$ |
| 45.1-a3 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{20} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$0.312771361$ |
$1956.885162$ |
3.29637 |
\( -\frac{1170502190383485568}{87890625} a^{5} + \frac{2369444969907304208}{87890625} a^{4} + \frac{672172040852308774}{17578125} a^{3} - \frac{4461956553521766476}{87890625} a^{2} - \frac{3714094569105967907}{87890625} a - \frac{113245323031240913}{17578125} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -3 a^{5} + a^{4} + 21 a^{3} - a^{2} - 34 a - 9\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( -224 a^{5} + 85 a^{4} + 1510 a^{3} - 80 a^{2} - 2302 a - 895\) , \( 1545 a^{5} - 573 a^{4} - 10410 a^{3} + 444 a^{2} + 15839 a + 6248\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}-a^{2}-34a-9\right){x}^{2}+\left(-224a^{5}+85a^{4}+1510a^{3}-80a^{2}-2302a-895\right){x}+1545a^{5}-573a^{4}-10410a^{3}+444a^{2}+15839a+6248$ |
| 45.1-a4 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$0.031277136$ |
$7827.540648$ |
3.29637 |
\( -\frac{4772564}{1215} a^{5} - \frac{11376679}{81} a^{4} - \frac{145900826}{1215} a^{3} + \frac{541506817}{1215} a^{2} + \frac{379895386}{1215} a + \frac{18685933}{405} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( a^{3} - 4 a - 2\) , \( a + 1\) , \( 6 a^{5} - a^{4} - 44 a^{3} - a^{2} + 73 a + 30\) , \( 5 a^{5} + 2 a^{4} - 31 a^{3} - 14 a^{2} + 35 a + 16\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(6a^{5}-a^{4}-44a^{3}-a^{2}+73a+30\right){x}+5a^{5}+2a^{4}-31a^{3}-14a^{2}+35a+16$ |
| 45.1-b1 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$962.3881611$ |
1.72772 |
\( -\frac{7123542098130361856}{15} a^{5} + \frac{1094487484828556022}{5} a^{4} + \frac{9670258293892248323}{3} a^{3} - \frac{8039599121866810022}{15} a^{2} - \frac{74653016232684779294}{15} a - 1030302127993585170 \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 686 a^{5} - 226 a^{4} - 4542 a^{3} + 352 a^{2} + 6572 a + 1376\) , \( 8264 a^{5} - 4931 a^{4} - 57506 a^{3} + 14498 a^{2} + 94248 a + 19342\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(a^{5}-7a^{3}-a^{2}+11a+4\right){x}^{2}+\left(686a^{5}-226a^{4}-4542a^{3}+352a^{2}+6572a+1376\right){x}+8264a^{5}-4931a^{4}-57506a^{3}+14498a^{2}+94248a+19342$ |
| 45.1-b2 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$60.14926007$ |
1.72772 |
\( \frac{974480916610807874048}{50625} a^{5} + \frac{2192578635875788926082}{50625} a^{4} - \frac{377615335888840389773}{10125} a^{3} - \frac{2065709568086390135938}{16875} a^{2} - \frac{358246336659862446862}{5625} a - \frac{86620748507289493126}{10125} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( 132 a^{5} - 252 a^{4} - 589 a^{3} + 1066 a^{2} + 151 a - 199\) , \( -9857 a^{5} + 12020 a^{4} + 53933 a^{3} - 45477 a^{2} - 50903 a - 9271\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}^{2}+\left(132a^{5}-252a^{4}-589a^{3}+1066a^{2}+151a-199\right){x}-9857a^{5}+12020a^{4}+53933a^{3}-45477a^{2}-50903a-9271$ |
| 45.1-b3 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3849.552644$ |
1.72772 |
\( -\frac{111388131328}{225} a^{5} + \frac{62867896343}{225} a^{4} + \frac{155339260534}{45} a^{3} - \frac{157390329971}{225} a^{2} - \frac{1225752719447}{225} a - \frac{50545458893}{45} \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 84 a^{5} - 45 a^{4} - 565 a^{3} + 105 a^{2} + 891 a + 212\) , \( 298 a^{5} - 153 a^{4} - 1998 a^{3} + 365 a^{2} + 3103 a + 667\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-29a-11\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a-3\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}+5a^{2}+32a+11\right){x}^{2}+\left(84a^{5}-45a^{4}-565a^{3}+105a^{2}+891a+212\right){x}+298a^{5}-153a^{4}-1998a^{3}+365a^{2}+3103a+667$ |
| 45.1-b4 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15398.21057$ |
1.72772 |
\( -\frac{252424}{15} a^{5} + \frac{27383}{5} a^{4} + \frac{338887}{3} a^{3} - \frac{171343}{15} a^{2} - \frac{2622451}{15} a - 36544 \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 19 a^{5} - 10 a^{4} - 135 a^{3} + 20 a^{2} + 231 a + 82\) , \( 21 a^{5} - 11 a^{4} - 150 a^{3} + 20 a^{2} + 261 a + 96\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-29a-11\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a-3\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}+5a^{2}+32a+11\right){x}^{2}+\left(19a^{5}-10a^{4}-135a^{3}+20a^{2}+231a+82\right){x}+21a^{5}-11a^{4}-150a^{3}+20a^{2}+261a+96$ |
| 45.1-c1 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{10} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2808.012961$ |
1.26026 |
\( \frac{814644996872}{253125} a^{5} + \frac{4632448800494}{759375} a^{4} - \frac{621554925707}{50625} a^{3} - \frac{23839748166988}{759375} a^{2} - \frac{13700111730136}{759375} a - \frac{392459283122}{151875} \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 6\) , \( -a^{5} + 8 a^{3} + a^{2} - 14 a - 3\) , \( a^{2} - 2\) , \( -28 a^{5} + 35 a^{4} + 155 a^{3} - 141 a^{2} - 139 a - 17\) , \( 120 a^{5} - 152 a^{4} - 644 a^{3} + 565 a^{2} + 598 a + 102\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-6\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+a^{2}-14a-3\right){x}^{2}+\left(-28a^{5}+35a^{4}+155a^{3}-141a^{2}-139a-17\right){x}+120a^{5}-152a^{4}-644a^{3}+565a^{2}+598a+102$ |
| 45.1-c2 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2808.012961$ |
1.26026 |
\( \frac{238856356}{5} a^{5} - \frac{936662147}{15} a^{4} - \frac{1274072207}{5} a^{3} + \frac{3613285261}{15} a^{2} + \frac{3305121649}{15} a + \frac{493348744}{15} \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 3 a^{2} - 54 a - 15\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 16\) , \( -21 a^{5} + 14 a^{4} + 133 a^{3} - 39 a^{2} - 183 a - 52\) , \( -32 a^{5} + 32 a^{4} + 187 a^{3} - 112 a^{2} - 214 a - 51\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-30a-12\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-16\right){y}={x}^{3}+\left(-5a^{5}+2a^{4}+34a^{3}-3a^{2}-54a-15\right){x}^{2}+\left(-21a^{5}+14a^{4}+133a^{3}-39a^{2}-183a-52\right){x}-32a^{5}+32a^{4}+187a^{3}-112a^{2}-214a-51$ |
| 45.1-c3 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{20} \cdot 5^{5} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$702.0032403$ |
1.26026 |
\( -\frac{2235207536722976741518}{7381125} a^{5} - \frac{3847491343375465224361}{7381125} a^{4} + \frac{9023716509726943142789}{7381125} a^{3} + \frac{20003053994412435317929}{7381125} a^{2} + \frac{1968846152941296134387}{1476225} a + \frac{1298548105637621590364}{7381125} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 7 a\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( -323 a^{5} + 73 a^{4} + 2251 a^{3} + 142 a^{2} - 3617 a - 1489\) , \( 1252 a^{5} - 284 a^{4} - 8725 a^{3} - 565 a^{2} + 14006 a + 5768\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-11a-5\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-18\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+7a\right){x}^{2}+\left(-323a^{5}+73a^{4}+2251a^{3}+142a^{2}-3617a-1489\right){x}+1252a^{5}-284a^{4}-8725a^{3}-565a^{2}+14006a+5768$ |
| 45.1-c4 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$702.0032403$ |
1.26026 |
\( \frac{767568164592729452}{45} a^{5} - \frac{967390709265225421}{45} a^{4} - \frac{4153706685300081856}{45} a^{3} + \frac{3699858317480481439}{45} a^{2} + \frac{756002343032818679}{9} a + \frac{609127105405722869}{45} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 3 a^{2} + 19 a + 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - a^{2} - 19 a - 8\) , \( 57 a^{5} - 41 a^{4} - 371 a^{3} + 103 a^{2} + 567 a + 110\) , \( 245 a^{5} - 68 a^{4} - 1745 a^{3} + 200 a^{2} + 2697 a + 559\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-10\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-a^{2}-19a-8\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+3a^{2}+19a+3\right){x}^{2}+\left(57a^{5}-41a^{4}-371a^{3}+103a^{2}+567a+110\right){x}+245a^{5}-68a^{4}-1745a^{3}+200a^{2}+2697a+559$ |
| 45.1-d1 |
45.1-d |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{2} \cdot 5^{7} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$366.7702968$ |
2.30454 |
\( \frac{1430847723840187894}{1875} a^{5} + \frac{2462936573108897663}{1875} a^{4} - \frac{5776449694269738587}{1875} a^{3} - \frac{4268257510246979394}{625} a^{2} - \frac{420112969221906737}{125} a - \frac{831253726470188812}{1875} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 3 a^{5} - a^{4} - 20 a^{3} + a^{2} + 29 a + 10\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( 16 a^{5} + 14 a^{4} - 78 a^{3} - 81 a^{2} + 6 a + 9\) , \( 55 a^{5} + 96 a^{4} - 224 a^{3} - 498 a^{2} - 233 a - 29\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){y}={x}^{3}+\left(3a^{5}-a^{4}-20a^{3}+a^{2}+29a+10\right){x}^{2}+\left(16a^{5}+14a^{4}-78a^{3}-81a^{2}+6a+9\right){x}+55a^{5}+96a^{4}-224a^{3}-498a^{2}-233a-29$ |
| 45.1-e1 |
45.1-e |
$2$ |
$2$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.010474223$ |
$41270.82159$ |
3.49220 |
\( -\frac{299322544022491}{3645} a^{5} + \frac{608425277207003}{3645} a^{4} + \frac{859340771116493}{3645} a^{3} - \frac{1149925182216842}{3645} a^{2} - \frac{191412328870237}{729} a - \frac{146365116009022}{3645} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 27 a^{4} - 294 a^{3} + 95 a^{2} + 461 a + 29\) , \( 159 a^{5} - 52 a^{4} - 1092 a^{3} + 30 a^{2} + 1716 a + 593\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-2a^{2}-23a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-3\right){x}^{2}+\left(43a^{5}-27a^{4}-294a^{3}+95a^{2}+461a+29\right){x}+159a^{5}-52a^{4}-1092a^{3}+30a^{2}+1716a+593$ |
| 45.1-e2 |
45.1-e |
$2$ |
$2$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.005237111$ |
$82541.64319$ |
3.49220 |
\( -\frac{337865}{9} a^{5} - \frac{8115143}{135} a^{4} + \frac{20010566}{45} a^{3} + \frac{2653301}{27} a^{2} - \frac{101043776}{135} a - \frac{23638802}{135} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 22 a^{4} - 294 a^{3} + 60 a^{2} + 461 a + 89\) , \( -176 a^{5} + 79 a^{4} + 1193 a^{3} - 187 a^{2} - 1836 a - 391\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-2a^{2}-23a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-3\right){x}^{2}+\left(43a^{5}-22a^{4}-294a^{3}+60a^{2}+461a+89\right){x}-176a^{5}+79a^{4}+1193a^{3}-187a^{2}-1836a-391$ |
| 45.1-f1 |
45.1-f |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{22} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1760.208474$ |
1.58000 |
\( \frac{2346897650445979}{885735} a^{5} - \frac{517584588238192}{885735} a^{4} - \frac{16313159822844242}{885735} a^{3} - \frac{121861357745033}{98415} a^{2} + \frac{1736751670938514}{59049} a + \frac{10685440990578398}{885735} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -2 a^{5} + 15 a^{3} + 3 a^{2} - 26 a - 9\) , \( -a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -8 a^{5} + 16 a^{4} + 55 a^{3} - 63 a^{2} - 100 a - 27\) , \( -40 a^{5} + 107 a^{4} + 230 a^{3} - 457 a^{2} - 316 a - 32\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}{y}+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){y}={x}^{3}+\left(-2a^{5}+15a^{3}+3a^{2}-26a-9\right){x}^{2}+\left(-8a^{5}+16a^{4}+55a^{3}-63a^{2}-100a-27\right){x}-40a^{5}+107a^{4}+230a^{3}-457a^{2}-316a-32$ |
| 45.1-g1 |
45.1-g |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{2} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004331393$ |
$144659.9245$ |
3.37458 |
\( \frac{647478001}{15} a^{5} - \frac{1315214113}{15} a^{4} - \frac{1860808178}{15} a^{3} + \frac{828316234}{5} a^{2} + 138294772 a + \frac{318834737}{15} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 9\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 4 a^{2} + 41 a + 13\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 3 a^{5} + a^{4} - 24 a^{3} - 11 a^{2} + 45 a + 23\) , \( 6 a^{5} - 4 a^{4} - 45 a^{3} + 9 a^{2} + 84 a + 32\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-9\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-27a^{3}+4a^{2}+41a+13\right){x}^{2}+\left(3a^{5}+a^{4}-24a^{3}-11a^{2}+45a+23\right){x}+6a^{5}-4a^{4}-45a^{3}+9a^{2}+84a+32$ |
*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.
