| 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 |
| 26.1-a1 |
26.1-a |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{20} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.047857006$ |
$27935.03020$ |
2.93369 |
\( \frac{19520264290701513}{13631488} a^{5} - \frac{12761723104756195}{6815744} a^{4} - \frac{41323862342475097}{6815744} a^{3} + \frac{6901581470480847}{1048576} a^{2} + \frac{18150681503595203}{6815744} a - \frac{29099518574411707}{13631488} \) |
\( \bigl[a^{5} - 4 a^{3} - a^{2} + a - 1\) , \( -a^{5} + 5 a^{3} + 2 a^{2} - 4 a - 3\) , \( a^{5} - 5 a^{3} + 5 a - 2\) , \( 149 a^{5} + 216 a^{4} - 703 a^{3} - 1153 a^{2} + 79 a + 317\) , \( 3055 a^{5} + 3281 a^{4} - 14232 a^{3} - 18426 a^{2} + 2076 a + 4981\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}-a^{2}+a-1\right){x}{y}+\left(a^{5}-5a^{3}+5a-2\right){y}={x}^{3}+\left(-a^{5}+5a^{3}+2a^{2}-4a-3\right){x}^{2}+\left(149a^{5}+216a^{4}-703a^{3}-1153a^{2}+79a+317\right){x}+3055a^{5}+3281a^{4}-14232a^{3}-18426a^{2}+2076a+4981$ |
| 26.1-a2 |
26.1-a |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{5} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.047857006$ |
$55870.06040$ |
2.93369 |
\( -\frac{1090939}{416} a^{5} + \frac{705305}{208} a^{4} + \frac{2111019}{208} a^{3} - \frac{265357}{32} a^{2} - \frac{1893977}{208} a + \frac{2887473}{416} \) |
\( \bigl[-a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 6\) , \( a^{4} - 4 a^{2} - a + 1\) , \( -a^{5} + a^{4} + 3 a^{3} - 2 a^{2} + 5\) , \( 2 a^{4} - a^{3} - 8 a^{2} + 4\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(2a^{4}-a^{3}-9a^{2}+6\right){x}^{2}+\left(-a^{5}+a^{4}+3a^{3}-2a^{2}+5\right){x}+2a^{4}-a^{3}-8a^{2}+4$ |
| 26.1-a3 |
26.1-a |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{10} \cdot 13^{2} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.023928503$ |
$111740.1208$ |
2.93369 |
\( -\frac{7521611163219}{173056} a^{5} + \frac{7034748606801}{86528} a^{4} + \frac{9426151102851}{86528} a^{3} - \frac{2138246823605}{13312} a^{2} - \frac{4150546552049}{86528} a + \frac{8087484844057}{173056} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 3 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{4} - 5 a^{2} + 4\) , \( -7 a^{5} - 6 a^{4} + 39 a^{3} + 38 a^{2} - 34 a - 31\) , \( 5 a^{5} - 29 a^{3} - 9 a^{2} + 34 a + 21\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+3a+3\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(-7a^{5}-6a^{4}+39a^{3}+38a^{2}-34a-31\right){x}+5a^{5}-29a^{3}-9a^{2}+34a+21$ |
| 26.1-a4 |
26.1-a |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{5} \cdot 13^{4} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.047857006$ |
$13967.51510$ |
2.93369 |
\( -\frac{33599985850365052139273}{913952} a^{5} + \frac{31385286842293812897667}{456976} a^{4} + \frac{42166846600278053746665}{456976} a^{3} - \frac{9534613318250318123759}{70304} a^{2} - \frac{18620042591940368039923}{456976} a + \frac{35971017115811810025595}{913952} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a\) , \( -60 a^{5} - 121 a^{4} + 87 a^{3} + 201 a^{2} - 20 a - 43\) , \( -1031 a^{5} - 2231 a^{4} + 1293 a^{3} + 3745 a^{2} - 2 a - 913\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-60a^{5}-121a^{4}+87a^{3}+201a^{2}-20a-43\right){x}-1031a^{5}-2231a^{4}+1293a^{3}+3745a^{2}-2a-913$ |
| 26.1-b1 |
26.1-b |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{11} \cdot 13^{4} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.321419408$ |
$1937.733043$ |
2.73348 |
\( \frac{357002408758786806802295}{58492928} a^{5} - \frac{235385891581882975695069}{29246464} a^{4} - \frac{760507941389341077455591}{29246464} a^{3} + \frac{126838816680165408982001}{4499456} a^{2} + \frac{340582673446053025087485}{29246464} a - \frac{541348346084446794242309}{58492928} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{3} - 2 a\) , \( 113 a^{5} + 48 a^{4} - 650 a^{3} - 390 a^{2} + 688 a + 397\) , \( 948 a^{5} + 499 a^{4} - 5462 a^{3} - 3821 a^{2} + 5768 a + 3997\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(113a^{5}+48a^{4}-650a^{3}-390a^{2}+688a+397\right){x}+948a^{5}+499a^{4}-5462a^{3}-3821a^{2}+5768a+3997$ |
| 26.1-b2 |
26.1-b |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{22} \cdot 13^{2} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.160709704$ |
$15501.86434$ |
2.73348 |
\( \frac{23047756799288365}{708837376} a^{5} - \frac{15119811297496111}{354418688} a^{4} - \frac{49031538678621949}{354418688} a^{3} + \frac{8160838129075915}{54525952} a^{2} + \frac{21945908426973327}{354418688} a - \frac{34841287528957799}{708837376} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{3} - 2 a\) , \( -37 a^{5} - 22 a^{4} + 215 a^{3} + 160 a^{2} - 232 a - 163\) , \( 197 a^{5} + 97 a^{4} - 1133 a^{3} - 757 a^{2} + 1195 a + 791\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(-37a^{5}-22a^{4}+215a^{3}+160a^{2}-232a-163\right){x}+197a^{5}+97a^{4}-1133a^{3}-757a^{2}+1195a+791$ |
| 26.1-b3 |
26.1-b |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{11} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.321419408$ |
$7750.932172$ |
2.73348 |
\( -\frac{1595629787}{26624} a^{5} + \frac{563455273}{13312} a^{4} + \frac{4464376459}{13312} a^{3} - \frac{365236973}{2048} a^{2} - \frac{5149313993}{13312} a + \frac{5767721649}{26624} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 3 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 2\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 3 a + 3\) , \( -3 a^{5} - 2 a^{4} + 15 a^{3} + 13 a^{2} - 9 a - 6\) , \( -4 a^{5} - 4 a^{4} + 20 a^{3} + 23 a^{2} - 9 a - 10\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-5a^{2}+3a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+3a+3\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-2\right){x}^{2}+\left(-3a^{5}-2a^{4}+15a^{3}+13a^{2}-9a-6\right){x}-4a^{5}-4a^{4}+20a^{3}+23a^{2}-9a-10$ |
| 26.1-b4 |
26.1-b |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{44} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.321419408$ |
$3875.466086$ |
2.73348 |
\( -\frac{991128891755822132791}{228698418577408} a^{5} - \frac{47658437141130054883}{114349209288704} a^{4} + \frac{1695824376933678158247}{114349209288704} a^{3} + \frac{226205964156186710223}{17592186044416} a^{2} + \frac{444132784334095214019}{114349209288704} a + \frac{167680252817805811013}{228698418577408} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 9 a^{2} - 4 a + 7\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -63 a^{5} - 133 a^{4} + 79 a^{3} + 212 a^{2} - 4 a - 45\) , \( -898 a^{5} - 1965 a^{4} + 1097 a^{3} + 3305 a^{2} + 34 a - 819\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-9a^{2}-4a+7\right){x}^{2}+\left(-63a^{5}-133a^{4}+79a^{3}+212a^{2}-4a-45\right){x}-898a^{5}-1965a^{4}+1097a^{3}+3305a^{2}+34a-819$ |
| 26.1-c1 |
26.1-c |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{11} \cdot 13^{4} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 11 \) |
$0.023543064$ |
$2610.681367$ |
5.93458 |
\( \frac{357002408758786806802295}{58492928} a^{5} - \frac{235385891581882975695069}{29246464} a^{4} - \frac{760507941389341077455591}{29246464} a^{3} + \frac{126838816680165408982001}{4499456} a^{2} + \frac{340582673446053025087485}{29246464} a - \frac{541348346084446794242309}{58492928} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -a^{5} + 4 a^{3} + 3 a^{2} - 2 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 3\) , \( 89 a^{5} + 15 a^{4} - 545 a^{3} - 120 a^{2} + 668 a + 17\) , \( 170 a^{5} - 575 a^{4} - 784 a^{3} + 2943 a^{2} + 781 a - 2945\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-a-3\right){y}={x}^{3}+\left(-a^{5}+4a^{3}+3a^{2}-2a-3\right){x}^{2}+\left(89a^{5}+15a^{4}-545a^{3}-120a^{2}+668a+17\right){x}+170a^{5}-575a^{4}-784a^{3}+2943a^{2}+781a-2945$ |
| 26.1-c2 |
26.1-c |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{22} \cdot 13^{2} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 11 \) |
$0.011771532$ |
$41770.90188$ |
5.93458 |
\( \frac{23047756799288365}{708837376} a^{5} - \frac{15119811297496111}{354418688} a^{4} - \frac{49031538678621949}{354418688} a^{3} + \frac{8160838129075915}{54525952} a^{2} + \frac{21945908426973327}{354418688} a - \frac{34841287528957799}{708837376} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( -a^{5} + 4 a^{3} + 3 a^{2} - 2 a - 3\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 3\) , \( -16 a^{5} - 5 a^{4} + 80 a^{3} + 65 a^{2} - 72 a - 83\) , \( -40 a^{5} - 6 a^{4} + 214 a^{3} + 104 a^{2} - 222 a - 119\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-a-3\right){y}={x}^{3}+\left(-a^{5}+4a^{3}+3a^{2}-2a-3\right){x}^{2}+\left(-16a^{5}-5a^{4}+80a^{3}+65a^{2}-72a-83\right){x}-40a^{5}-6a^{4}+214a^{3}+104a^{2}-222a-119$ |
| 26.1-c3 |
26.1-c |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{11} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 11 \) |
$0.005885766$ |
$83541.80376$ |
5.93458 |
\( -\frac{1595629787}{26624} a^{5} + \frac{563455273}{13312} a^{4} + \frac{4464376459}{13312} a^{3} - \frac{365236973}{2048} a^{2} - \frac{5149313993}{13312} a + \frac{5767721649}{26624} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 4 a + 2\) , \( -a^{5} + 3 a^{3} + 4 a^{2} - 4\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - 5 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{5}+a^{4}-5a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-a^{5}+3a^{3}+4a^{2}-4\right){x}-a^{5}+a^{4}+4a^{3}-4a^{2}-5a+2$ |
| 26.1-c4 |
26.1-c |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{44} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 11 \) |
$0.023543064$ |
$5221.362735$ |
5.93458 |
\( -\frac{991128891755822132791}{228698418577408} a^{5} - \frac{47658437141130054883}{114349209288704} a^{4} + \frac{1695824376933678158247}{114349209288704} a^{3} + \frac{226205964156186710223}{17592186044416} a^{2} + \frac{444132784334095214019}{114349209288704} a + \frac{167680252817805811013}{228698418577408} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 4 a + 3\) , \( -a^{5} - a^{4} + 6 a^{3} + 6 a^{2} - 7 a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( -17 a^{5} - 4 a^{4} + 56 a^{3} - 8 a^{2} - 23 a + 10\) , \( 38 a^{5} + 34 a^{4} - 85 a^{3} - 19 a^{2} + 21 a + 1\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-6a^{2}+4a+3\right){x}{y}+\left(-a^{4}+a^{3}+4a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+6a^{2}-7a-3\right){x}^{2}+\left(-17a^{5}-4a^{4}+56a^{3}-8a^{2}-23a+10\right){x}+38a^{5}+34a^{4}-85a^{3}-19a^{2}+21a+1$ |
| 26.1-d1 |
26.1-d |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{20} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.076933205$ |
$3351.968531$ |
5.65892 |
\( \frac{19520264290701513}{13631488} a^{5} - \frac{12761723104756195}{6815744} a^{4} - \frac{41323862342475097}{6815744} a^{3} + \frac{6901581470480847}{1048576} a^{2} + \frac{18150681503595203}{6815744} a - \frac{29099518574411707}{13631488} \) |
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( -a^{5} + 6 a^{3} - 6 a + 2\) , \( a^{2} - 2\) , \( 777 a^{5} + 900 a^{4} - 3625 a^{3} - 4983 a^{2} + 483 a + 1355\) , \( -24261 a^{5} - 27965 a^{4} + 113303 a^{3} + 154884 a^{2} - 15468 a - 42077\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-6a+2\right){x}^{2}+\left(777a^{5}+900a^{4}-3625a^{3}-4983a^{2}+483a+1355\right){x}-24261a^{5}-27965a^{4}+113303a^{3}+154884a^{2}-15468a-42077$ |
| 26.1-d2 |
26.1-d |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{5} \cdot 13 \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.019233301$ |
$53631.49649$ |
5.65892 |
\( -\frac{1090939}{416} a^{5} + \frac{705305}{208} a^{4} + \frac{2111019}{208} a^{3} - \frac{265357}{32} a^{2} - \frac{1893977}{208} a + \frac{2887473}{416} \) |
\( \bigl[a^{5} - 5 a^{3} - a^{2} + 4 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a + 2\) , \( -a^{5} - 3 a^{4} + 4 a^{2} + a - 1\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-a^{2}+4a+1\right){x}{y}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){x}^{2}+\left(a+2\right){x}-a^{5}-3a^{4}+4a^{2}+a-1$ |
| 26.1-d3 |
26.1-d |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{10} \cdot 13^{2} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.038466602$ |
$26815.74824$ |
5.65892 |
\( -\frac{7521611163219}{173056} a^{5} + \frac{7034748606801}{86528} a^{4} + \frac{9426151102851}{86528} a^{3} - \frac{2138246823605}{13312} a^{2} - \frac{4150546552049}{86528} a + \frac{8087484844057}{173056} \) |
\( \bigl[a^{5} - 4 a^{3} - 2 a^{2} + 2 a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 7 a^{2} + 2 a + 4\) , \( a^{5} - 4 a^{3} - 2 a^{2} + 2 a + 2\) , \( -16 a^{5} - 8 a^{4} + 90 a^{3} + 60 a^{2} - 94 a - 62\) , \( -72 a^{5} - 35 a^{4} + 412 a^{3} + 274 a^{2} - 436 a - 288\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}-2a^{2}+2a+1\right){x}{y}+\left(a^{5}-4a^{3}-2a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-7a^{2}+2a+4\right){x}^{2}+\left(-16a^{5}-8a^{4}+90a^{3}+60a^{2}-94a-62\right){x}-72a^{5}-35a^{4}+412a^{3}+274a^{2}-436a-288$ |
| 26.1-d4 |
26.1-d |
$4$ |
$4$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{5} \cdot 13^{4} \) |
$160.27067$ |
$(a), (-a^4+4a^2-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 5 \) |
$0.076933205$ |
$1675.984265$ |
5.65892 |
\( -\frac{33599985850365052139273}{913952} a^{5} + \frac{31385286842293812897667}{456976} a^{4} + \frac{42166846600278053746665}{456976} a^{3} - \frac{9534613318250318123759}{70304} a^{2} - \frac{18620042591940368039923}{456976} a + \frac{35971017115811810025595}{913952} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -26 a^{5} + a^{4} + 122 a^{3} - 35 a^{2} - 131 a + 62\) , \( 258 a^{5} - 81 a^{4} - 1305 a^{3} + 485 a^{2} + 1426 a - 672\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-26a^{5}+a^{4}+122a^{3}-35a^{2}-131a+62\right){x}+258a^{5}-81a^{4}-1305a^{3}+485a^{2}+1426a-672$ |
*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.
