| 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 |
| 145.1-a1 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( \frac{3563292375597999624077197170209907}{121945} a^{3} - \frac{861644665597441997023740310528629}{24389} a^{2} - \frac{13352505574615280750900341346722352}{121945} a + \frac{3408920655873324332116393023886101}{24389} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( -571 a^{3} + 533 a^{2} + 2618 a - 3120\) , \( 17430 a^{3} - 24276 a^{2} - 55306 a + 75770\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-571a^{3}+533a^{2}+2618a-3120\right){x}+17430a^{3}-24276a^{2}-55306a+75770$ |
| 145.1-a2 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$10.57383297$ |
1.261003163 |
\( \frac{158027113641077297281505009}{44226847900683630125} a^{3} - \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{592761089347624947777619984}{44226847900683630125} a + \frac{771813679690725336739721491}{44226847900683630125} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( -71 a^{3} + 153 a^{2} + 68 a - 220\) , \( 178 a^{3} + 102 a^{2} - 1348 a + 1136\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-71a^{3}+153a^{2}+68a-220\right){x}+178a^{3}+102a^{2}-1348a+1136$ |
| 145.1-a3 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$169.1813275$ |
1.261003163 |
\( \frac{1083430848406723361809622}{14870583025} a^{3} - \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{4059873541335931022491667}{14870583025} a + \frac{5182468070047739037028313}{14870583025} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( -41 a^{3} + 23 a^{2} + 183 a - 190\) , \( 294 a^{3} - 369 a^{2} - 959 a + 1239\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-41a^{3}+23a^{2}+183a-190\right){x}+294a^{3}-369a^{2}-959a+1239$ |
| 145.1-a4 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$10.57383297$ |
1.261003163 |
\( -\frac{5931064353506353713299}{3536405} a^{3} - \frac{2006249020931218366527}{3536405} a^{2} + \frac{21039372166278616600824}{3536405} a + \frac{4431918296036025658078}{3536405} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( 14 a^{3} - 7 a^{2} - 27 a - 10\) , \( 64 a^{3} - 114 a^{2} - 9 a + 4\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(14a^{3}-7a^{2}-27a-10\right){x}+64a^{3}-114a^{2}-9a+4$ |
| 145.1-a5 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( \frac{5570253978166843}{121945} a^{3} + \frac{921603439957079}{24389} a^{2} - \frac{13862863581255898}{121945} a - \frac{610213584699644}{24389} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( -6 a^{3} - 17 a^{2} + 38 a - 5\) , \( 9 a^{3} + 30 a^{2} - 65 a + 12\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-6a^{3}-17a^{2}+38a-5\right){x}+9a^{3}+30a^{2}-65a+12$ |
| 145.1-a6 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( \frac{593751}{145} a^{3} + \frac{571893}{145} a^{2} - \frac{2254932}{145} a - \frac{491089}{145} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( -a^{3} + 3 a^{2} - 2 a\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-a^{3}+3a^{2}-2a\right){x}$ |
| 145.1-a7 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$169.1813275$ |
1.261003163 |
\( -\frac{131170515684}{4205} a^{3} + \frac{28514711139}{4205} a^{2} + \frac{69448214349}{841} a + \frac{70461685372}{4205} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( 4 a^{3} - 12 a^{2} + 8 a\) , \( 41 a^{3} - 120 a^{2} + 69 a + 23\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(4a^{3}-12a^{2}+8a\right){x}+41a^{3}-120a^{2}+69a+23$ |
| 145.1-a8 |
145.1-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( -\frac{87603065803054601}{145} a^{3} + \frac{258980786426845107}{145} a^{2} - \frac{156230898365218968}{145} a - \frac{44779476849982326}{145} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 0\) , \( 74 a^{3} - 257 a^{2} + 203 a + 10\) , \( 1822 a^{3} - 5406 a^{2} + 3183 a + 1054\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(74a^{3}-257a^{2}+203a+10\right){x}+1822a^{3}-5406a^{2}+3183a+1054$ |
| 145.1-b1 |
145.1-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( \frac{20885181}{725} a^{3} - \frac{26043186}{725} a^{2} - \frac{78162292}{725} a + \frac{20490856}{145} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( 3 a^{2} - a - 7\) , \( a^{3} + 2 a^{2} - 4 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(3a^{2}-a-7\right){x}+a^{3}+2a^{2}-4a-5$ |
| 145.1-b2 |
145.1-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( -\frac{57083181404}{525625} a^{3} + \frac{173419982887}{525625} a^{2} - \frac{106479911684}{525625} a - \frac{6075097893}{105125} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( -10 a^{3} - 2 a^{2} + 34 a + 3\) , \( -9 a^{3} - 2 a^{2} + 31 a - 2\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-10a^{3}-2a^{2}+34a+3\right){x}-9a^{3}-2a^{2}+31a-2$ |
| 145.1-b3 |
145.1-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( -\frac{127460459953705744354635337823}{86249381545} a^{3} - \frac{43114930005051581253212843029}{86249381545} a^{2} + \frac{452142801599258433081453134591}{86249381545} a + \frac{95243335102582476759197612687}{86249381545} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -16838 a^{3} - 21557 a^{2} + 25365 a + 6059\) , \( 3201633 a^{3} + 3227005 a^{2} - 6714610 a - 1515432\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a-1\right){x}^{2}+\left(-16838a^{3}-21557a^{2}+25365a+6059\right){x}+3201633a^{3}+3227005a^{2}-6714610a-1515432$ |
| 145.1-b4 |
145.1-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( \frac{3820306162743415739267889753693269}{1487791163378997317405} a^{3} + \frac{3159218411003952357936457867154706}{1487791163378997317405} a^{2} - \frac{1901869393364452258762849674383914}{297558232675799463481} a - \frac{2091162665226349776296224737575132}{1487791163378997317405} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -503858 a^{3} - 424367 a^{2} + 1237475 a + 272614\) , \( 278727121 a^{3} + 231111633 a^{2} - 692450628 a - 152315529\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a-1\right){x}^{2}+\left(-503858a^{3}-424367a^{2}+1237475a+272614\right){x}+278727121a^{3}+231111633a^{2}-692450628a-152315529$ |
| 145.1-c1 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( \frac{3563292375597999624077197170209907}{121945} a^{3} - \frac{861644665597441997023740310528629}{24389} a^{2} - \frac{13352505574615280750900341346722352}{121945} a + \frac{3408920655873324332116393023886101}{24389} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -10292 a^{3} + 12520 a^{2} + 38585 a - 49539\) , \( -948241 a^{3} + 1146819 a^{2} + 3553297 a - 4536988\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-10292a^{3}+12520a^{2}+38585a-49539\right){x}-948241a^{3}+1146819a^{2}+3553297a-4536988$ |
| 145.1-c2 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( \frac{158027113641077297281505009}{44226847900683630125} a^{3} - \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{592761089347624947777619984}{44226847900683630125} a + \frac{771813679690725336739721491}{44226847900683630125} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -602 a^{3} + 800 a^{2} + 2255 a - 3129\) , \( -14993 a^{3} + 17699 a^{2} + 56109 a - 70194\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-602a^{3}+800a^{2}+2255a-3129\right){x}-14993a^{3}+17699a^{2}+56109a-70194$ |
| 145.1-c3 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$14.42414881$ |
0.967601317 |
\( \frac{1083430848406723361809622}{14870583025} a^{3} - \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{4059873541335931022491667}{14870583025} a + \frac{5182468070047739037028313}{14870583025} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -647 a^{3} + 780 a^{2} + 2420 a - 3094\) , \( -14729 a^{3} + 17785 a^{2} + 55183 a - 70391\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-647a^{3}+780a^{2}+2420a-3094\right){x}-14729a^{3}+17785a^{2}+55183a-70391$ |
| 145.1-c4 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( -\frac{87603065803054601}{145} a^{3} + \frac{258980786426845107}{145} a^{2} - \frac{156230898365218968}{145} a - \frac{44779476849982326}{145} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -127 a^{3} + 145 a^{2} + 485 a - 609\) , \( -1287 a^{3} + 1556 a^{2} + 4797 a - 6107\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-127a^{3}+145a^{2}+485a-609\right){x}-1287a^{3}+1556a^{2}+4797a-6107$ |
| 145.1-c5 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.42414881$ |
0.967601317 |
\( \frac{5570253978166843}{121945} a^{3} + \frac{921603439957079}{24389} a^{2} - \frac{13862863581255898}{121945} a - \frac{610213584699644}{24389} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -47 a^{3} + 45 a^{2} + 170 a - 189\) , \( -230 a^{3} + 263 a^{2} + 853 a - 1066\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-47a^{3}+45a^{2}+170a-189\right){x}-230a^{3}+263a^{2}+853a-1066$ |
| 145.1-c6 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( -\frac{5931064353506353713299}{3536405} a^{3} - \frac{2006249020931218366527}{3536405} a^{2} + \frac{21039372166278616600824}{3536405} a + \frac{4431918296036025658078}{3536405} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 33 a^{3} + 35 a^{2} - 115 a - 109\) , \( -239 a^{3} - 120 a^{2} + 843 a + 319\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(33a^{3}+35a^{2}-115a-109\right){x}-239a^{3}-120a^{2}+843a+319$ |
| 145.1-c7 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1168.356053$ |
0.967601317 |
\( -\frac{131170515684}{4205} a^{3} + \frac{28514711139}{4205} a^{2} + \frac{69448214349}{841} a + \frac{70461685372}{4205} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -7 a^{3} + 10 a^{2} + 25 a - 39\) , \( -25 a^{3} + 20 a^{2} + 92 a - 84\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-7a^{3}+10a^{2}+25a-39\right){x}-25a^{3}+20a^{2}+92a-84$ |
| 145.1-c8 |
145.1-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1168.356053$ |
0.967601317 |
\( \frac{593751}{145} a^{3} + \frac{571893}{145} a^{2} - \frac{2254932}{145} a - \frac{491089}{145} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -2 a^{3} + 5 a + 1\) , \( -a^{3} + a^{2} + 3 a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-2a^{3}+5a+1\right){x}-a^{3}+a^{2}+3a-4$ |
| 145.1-d1 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.417791016$ |
1.068112419 |
\( -\frac{127460459953705744354635337823}{86249381545} a^{3} - \frac{43114930005051581253212843029}{86249381545} a^{2} + \frac{452142801599258433081453134591}{86249381545} a + \frac{95243335102582476759197612687}{86249381545} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( 1\) , \( a^{3} - 2 a\) , \( -70933 a^{3} - 60234 a^{2} + 173150 a + 38181\) , \( -15136874 a^{3} - 12573990 a^{2} + 37555267 a + 8262428\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+{x}^{2}+\left(-70933a^{3}-60234a^{2}+173150a+38181\right){x}-15136874a^{3}-12573990a^{2}+37555267a+8262428$ |
| 145.1-d2 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$0.104447754$ |
1.068112419 |
\( \frac{3820306162743415739267889753693269}{1487791163378997317405} a^{3} + \frac{3159218411003952357936457867154706}{1487791163378997317405} a^{2} - \frac{1901869393364452258762849674383914}{297558232675799463481} a - \frac{2091162665226349776296224737575132}{1487791163378997317405} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( 1\) , \( a^{3} - 2 a\) , \( -1183108 a^{3} - 980109 a^{2} + 2941170 a + 646896\) , \( -967645656 a^{3} - 800385364 a^{2} + 2408187431 a + 529587766\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+{x}^{2}+\left(-1183108a^{3}-980109a^{2}+2941170a+646896\right){x}-967645656a^{3}-800385364a^{2}+2408187431a+529587766$ |
| 145.1-d3 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( \frac{20885181}{725} a^{3} - \frac{26043186}{725} a^{2} - \frac{78162292}{725} a + \frac{20490856}{145} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a + 1\) , \( a^{3} + 2 a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{3}-a+1\right){x}+a^{3}+2a^{2}-4a-1$ |
| 145.1-d4 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( -\frac{57083181404}{525625} a^{3} + \frac{173419982887}{525625} a^{2} - \frac{106479911684}{525625} a - \frac{6075097893}{105125} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - 15 a^{2} + 19 a + 6\) , \( -19 a^{3} + 48 a^{2} - 22 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{3}-15a^{2}+19a+6\right){x}-19a^{3}+48a^{2}-22a-7$ |
| 145.1-e1 |
145.1-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.00786948$ |
1.193508078 |
\( \frac{1895130882734167707118525176}{3536405} a^{3} - \frac{2291321120460720703238799999}{3536405} a^{2} - \frac{7101506979787718340676932788}{3536405} a + \frac{9065142753900138024018979693}{3536405} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -13 a^{3} + 133 a^{2} + 61 a - 484\) , \( -2909 a^{3} - 665 a^{2} + 8702 a - 2209\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-13a^{3}+133a^{2}+61a-484\right){x}-2909a^{3}-665a^{2}+8702a-2209$ |
| 145.1-e2 |
145.1-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$40.03147792$ |
1.193508078 |
\( -\frac{1220610937193766735514264216}{145} a^{3} - \frac{412885335871671877657434893}{145} a^{2} + \frac{4329895318478081718741496612}{145} a + \frac{912087211072173548706508999}{145} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -93 a^{3} - 687 a^{2} - 1109 a - 234\) , \( -67039 a^{3} - 41297 a^{2} + 197456 a + 42415\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-93a^{3}-687a^{2}-1109a-234\right){x}-67039a^{3}-41297a^{2}+197456a+42415$ |
| 145.1-e3 |
145.1-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$160.1259116$ |
1.193508078 |
\( -\frac{7687159294137043}{4205} a^{3} - \frac{2664464498192138}{4205} a^{2} + \frac{27260504930559828}{4205} a + \frac{5973600272646728}{4205} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -13 a^{3} - 37 a^{2} - 44 a - 39\) , \( -1144 a^{3} - 675 a^{2} + 3401 a + 673\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-13a^{3}-37a^{2}-44a-39\right){x}-1144a^{3}-675a^{2}+3401a+673$ |
| 145.1-e4 |
145.1-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$640.5036467$ |
1.193508078 |
\( -\frac{335501373859}{145} a^{3} + \frac{992240865343}{145} a^{2} - \frac{598958618337}{145} a - \frac{171681225789}{145} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -8 a^{3} - 7 a^{2} + 16 a + 1\) , \( -4 a^{3} + 3 a^{2} + 22 a + 3\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-8a^{3}-7a^{2}+16a+1\right){x}-4a^{3}+3a^{2}+22a+3$ |
| 145.1-f1 |
145.1-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( \frac{1895130882734167707118525176}{3536405} a^{3} - \frac{2291321120460720703238799999}{3536405} a^{2} - \frac{7101506979787718340676932788}{3536405} a + \frac{9065142753900138024018979693}{3536405} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( -400 a^{3} + 537 a^{2} + 1505 a - 2104\) , \( 8354 a^{3} - 9885 a^{2} - 31265 a + 39200\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-400a^{3}+537a^{2}+1505a-2104\right){x}+8354a^{3}-9885a^{2}-31265a+39200$ |
| 145.1-f2 |
145.1-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( -\frac{1220610937193766735514264216}{145} a^{3} - \frac{412885335871671877657434893}{145} a^{2} + \frac{4329895318478081718741496612}{145} a + \frac{912087211072173548706508999}{145} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 490 a^{3} + 187 a^{2} - 1775 a - 524\) , \( 8376 a^{3} + 2719 a^{2} - 29553 a - 5506\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(490a^{3}+187a^{2}-1775a-524\right){x}+8376a^{3}+2719a^{2}-29553a-5506$ |
| 145.1-f3 |
145.1-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( -\frac{7687159294137043}{4205} a^{3} - \frac{2664464498192138}{4205} a^{2} + \frac{27260504930559828}{4205} a + \frac{5973600272646728}{4205} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 5 a^{3} + 42 a^{2} - 15 a - 154\) , \( 261 a^{3} - 113 a^{2} - 949 a + 525\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{3}+42a^{2}-15a-154\right){x}+261a^{3}-113a^{2}-949a+525$ |
| 145.1-f4 |
145.1-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( -\frac{335501373859}{145} a^{3} + \frac{992240865343}{145} a^{2} - \frac{598958618337}{145} a - \frac{171681225789}{145} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 2 a^{2} - 9\) , \( 4 a^{3} - 3 a^{2} - 14 a + 9\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a^{2}-9\right){x}+4a^{3}-3a^{2}-14a+9$ |
*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.
