| 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 |
| 145.3-a1 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( -\frac{765623948004282479}{145} a^{3} - \frac{258980786426845107}{145} a^{2} + \frac{2715911939787230208}{145} a + \frac{572103573083015331}{145} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 767 a^{3} + 261 a^{2} - 2731 a - 600\) , \( 14439 a^{3} + 4899 a^{2} - 51204 a - 10817\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(767a^{3}+261a^{2}-2731a-600\right){x}+14439a^{3}+4899a^{2}-51204a-10817$ |
| 145.3-a2 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( \frac{5208887255763927730527148886760421}{121945} a^{3} + \frac{861644665597441997023740310528629}{24389} a^{2} - \frac{12964033319470501312912696824188632}{121945} a - \frac{2850918480403500158561590927234706}{121945} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( -188 a^{3} - 529 a^{2} - 346 a - 90\) , \( 35387 a^{3} + 22219 a^{2} - 103338 a - 22206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-188a^{3}-529a^{2}-346a-90\right){x}+35387a^{3}+22219a^{2}-103338a-22206$ |
| 145.3-a3 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( \frac{3810135131626079}{121945} a^{3} - \frac{921603439957079}{24389} a^{2} - \frac{14278303748122868}{121945} a + \frac{18228899228887991}{121945} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 42 a^{3} + 21 a^{2} - 151 a - 60\) , \( -142 a^{3} - 72 a^{2} + 501 a + 193\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(42a^{3}+21a^{2}-151a-60\right){x}-142a^{3}-72a^{2}+501a+193$ |
| 145.3-a4 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( \frac{1583779420652621584630444}{14870583025} a^{3} + \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{3941757265842103816828531}{14870583025} a - \frac{173366239902931707913796}{2974116605} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 7 a^{3} - 19 a^{2} - 86 a - 45\) , \( 353 a^{3} + 222 a^{2} - 980 a - 125\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(7a^{3}-19a^{2}-86a-45\right){x}+353a^{3}+222a^{2}-980a-125$ |
| 145.3-a5 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( -\frac{41191140426}{841} a^{3} - \frac{28514711139}{4205} a^{2} + \frac{664137581697}{4205} a + \frac{138250054621}{4205} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 47 a^{3} + 16 a^{2} - 166 a - 35\) , \( 275 a^{3} + 93 a^{2} - 975 a - 206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(47a^{3}+16a^{2}-166a-35\right){x}+275a^{3}+93a^{2}-975a-206$ |
| 145.3-a6 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$10.57383297$ |
1.261003163 |
\( -\frac{135727245363115977169}{707281} a^{3} + \frac{2006249020931218366527}{3536405} a^{2} - \frac{1210270425312815803392}{3536405} a - \frac{346898681929292347103}{3536405} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 47 a^{3} + 11 a^{2} - 161 a - 30\) , \( 283 a^{3} + 87 a^{2} - 990 a - 215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(47a^{3}+11a^{2}-161a-30\right){x}+283a^{3}+87a^{2}-990a-215$ |
| 145.3-a7 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( -\frac{451821}{145} a^{3} - \frac{571893}{145} a^{2} + \frac{1829142}{145} a + \frac{1322804}{145} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 2 a^{3} + a^{2} - 6 a\) , \( 7 a^{3} + 3 a^{2} - 24 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(2a^{3}+a^{2}-6a\right){x}+7a^{3}+3a^{2}-24a-6$ |
| 145.3-a8 |
145.3-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( \frac{234852755657943296835935447}{44226847900683630125} a^{3} + \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{585878518549436834574701384}{44226847900683630125} a - \frac{128887630498703941143525046}{44226847900683630125} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( -358 a^{3} - 149 a^{2} + 1214 a + 240\) , \( -301 a^{3} - 19 a^{2} + 1354 a + 404\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-358a^{3}-149a^{2}+1214a+240\right){x}-301a^{3}-19a^{2}+1354a+404$ |
| 145.3-b1 |
145.3-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( \frac{522531854629489861064170555139760}{297558232675799463481} a^{3} - \frac{3159218411003952357936457867154706}{1487791163378997317405} a^{2} - \frac{9789549340850333839951979216256637}{1487791163378997317405} a + \frac{12497282500197445579439027620203929}{1487791163378997317405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 2\) , \( -233588 a^{3} - 193414 a^{2} + 580871 a + 127682\) , \( 85052980 a^{3} + 70349831 a^{2} - 211675141 a - 46549371\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-233588a^{3}-193414a^{2}+580871a+127682\right){x}+85052980a^{3}+70349831a^{2}-211675141a-46549371$ |
| 145.3-b2 |
145.3-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( -\frac{14584108210512963083875373672}{86249381545} a^{3} + \frac{43114930005051581253212843029}{86249381545} a^{2} - \frac{26009097106602310765921000106}{86249381545} a - \frac{7454963179482648236106638307}{86249381545} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 2\) , \( -234588 a^{3} - 194044 a^{2} + 583826 a + 128387\) , \( 84635877 a^{3} + 70001639 a^{2} - 210644160 a - 46322722\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-234588a^{3}-194044a^{2}+583826a+128387\right){x}+84635877a^{3}+70001639a^{2}-210644160a-46322722$ |
| 145.3-b3 |
145.3-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( -\frac{508232620187}{525625} a^{3} - \frac{173419982887}{525625} a^{2} + \frac{1802427316457}{525625} a + \frac{385574986187}{525625} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} - 5 a - 6\) , \( -3 a^{3} + 2 a^{2} + 4 a - 3\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(5a^{2}-5a-6\right){x}-3a^{3}+2a^{2}+4a-3$ |
| 145.3-b4 |
145.3-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( \frac{31421618}{725} a^{3} + \frac{26043186}{725} a^{2} - \frac{15751621}{145} a - \frac{17225213}{725} \) |
\( \bigl[a^{2} + a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( -1\) , \( -2 a^{3} - 2 a^{2} + 6 a\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}-{x}-2a^{3}-2a^{2}+6a$ |
| 145.3-c1 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1168.356053$ |
0.967601317 |
\( -\frac{451821}{145} a^{3} - \frac{571893}{145} a^{2} + \frac{1829142}{145} a + \frac{1322804}{145} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( -3 a^{3} - 2 a^{2} + 8 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-a^{3}-a^{2}+3a+3\right){x}-3a^{3}-2a^{2}+8a+1$ |
| 145.3-c2 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( -\frac{41191140426}{841} a^{3} - \frac{28514711139}{4205} a^{2} + \frac{664137581697}{4205} a + \frac{138250054621}{4205} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -11 a^{3} - 11 a^{2} + 28 a + 8\) , \( -44 a^{3} - 36 a^{2} + 109 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-11a^{3}-11a^{2}+28a+8\right){x}-44a^{3}-36a^{2}+109a+24$ |
| 145.3-c3 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( -\frac{135727245363115977169}{707281} a^{3} + \frac{2006249020931218366527}{3536405} a^{2} - \frac{1210270425312815803392}{3536405} a - \frac{346898681929292347103}{3536405} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -16 a^{3} - 36 a^{2} + 63 a + 18\) , \( -14 a^{3} + 64 a^{2} - 50 a - 14\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-16a^{3}-36a^{2}+63a+18\right){x}-14a^{3}+64a^{2}-50a-14$ |
| 145.3-c4 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.42414881$ |
0.967601317 |
\( \frac{3810135131626079}{121945} a^{3} - \frac{921603439957079}{24389} a^{2} - \frac{14278303748122868}{121945} a + \frac{18228899228887991}{121945} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -61 a^{3} - 46 a^{2} + 153 a + 23\) , \( -406 a^{3} - 334 a^{2} + 1009 a + 215\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-61a^{3}-46a^{2}+153a+23\right){x}-406a^{3}-334a^{2}+1009a+215$ |
| 145.3-c5 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( -\frac{765623948004282479}{145} a^{3} - \frac{258980786426845107}{145} a^{2} + \frac{2715911939787230208}{145} a + \frac{572103573083015331}{145} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -166 a^{3} - 146 a^{2} + 393 a + 78\) , \( -2158 a^{3} - 1772 a^{2} + 5412 a + 1214\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-166a^{3}-146a^{2}+393a+78\right){x}-2158a^{3}-1772a^{2}+5412a+1214$ |
| 145.3-c6 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( \frac{1583779420652621584630444}{14870583025} a^{3} + \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{3941757265842103816828531}{14870583025} a - \frac{173366239902931707913796}{2974116605} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -946 a^{3} - 781 a^{2} + 2358 a + 508\) , \( -22779 a^{3} - 18841 a^{2} + 56695 a + 12461\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-946a^{3}-781a^{2}+2358a+508\right){x}-22779a^{3}-18841a^{2}+56695a+12461$ |
| 145.3-c7 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( \frac{234852755657943296835935447}{44226847900683630125} a^{3} + \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{585878518549436834574701384}{44226847900683630125} a - \frac{128887630498703941143525046}{44226847900683630125} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -951 a^{3} - 801 a^{2} + 2403 a + 523\) , \( -22813 a^{3} - 18780 a^{2} + 56708 a + 12443\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-951a^{3}-801a^{2}+2403a+523\right){x}-22813a^{3}-18780a^{2}+56708a+12443$ |
| 145.3-c8 |
145.3-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( \frac{5208887255763927730527148886760421}{121945} a^{3} + \frac{861644665597441997023740310528629}{24389} a^{2} - \frac{12964033319470501312912696824188632}{121945} a - \frac{2850918480403500158561590927234706}{121945} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -15101 a^{3} - 12521 a^{2} + 37593 a + 8253\) , \( -1406717 a^{3} - 1163610 a^{2} + 3501286 a + 769983\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-15101a^{3}-12521a^{2}+37593a+8253\right){x}-1406717a^{3}-1163610a^{2}+3501286a+769983$ |
| 145.3-d1 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( \frac{522531854629489861064170555139760}{297558232675799463481} a^{3} - \frac{3159218411003952357936457867154706}{1487791163378997317405} a^{2} - \frac{9789549340850333839951979216256637}{1487791163378997317405} a + \frac{12497282500197445579439027620203929}{1487791163378997317405} \) |
\( \bigl[a^{2} - 2\) , \( 1\) , \( a^{3} - 3 a\) , \( 1238 a^{3} - 6845 a^{2} - 20213 a - 4081\) , \( -124141 a^{3} - 718644 a^{2} - 1025357 a - 185029\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+{x}^{2}+\left(1238a^{3}-6845a^{2}-20213a-4081\right){x}-124141a^{3}-718644a^{2}-1025357a-185029$ |
| 145.3-d2 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.417791016$ |
1.068112419 |
\( -\frac{14584108210512963083875373672}{86249381545} a^{3} + \frac{43114930005051581253212843029}{86249381545} a^{2} - \frac{26009097106602310765921000106}{86249381545} a - \frac{7454963179482648236106638307}{86249381545} \) |
\( \bigl[a^{2} - 2\) , \( 1\) , \( a^{3} - 3 a\) , \( -13997 a^{3} - 12060 a^{2} + 33787 a + 7454\) , \( -1357190 a^{3} - 1132664 a^{2} + 3355843 a + 738645\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+{x}^{2}+\left(-13997a^{3}-12060a^{2}+33787a+7454\right){x}-1357190a^{3}-1132664a^{2}+3355843a+738645$ |
| 145.3-d3 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
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 |
\( -\frac{508232620187}{525625} a^{3} - \frac{173419982887}{525625} a^{2} + \frac{1802427316457}{525625} a + \frac{385574986187}{525625} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 36 a^{3} + 18 a^{2} - 134 a - 36\) , \( -153 a^{3} - 50 a^{2} + 535 a + 122\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(36a^{3}+18a^{2}-134a-36\right){x}-153a^{3}-50a^{2}+535a+122$ |
| 145.3-d4 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( \frac{31421618}{725} a^{3} + \frac{26043186}{725} a^{2} - \frac{15751621}{145} a - \frac{17225213}{725} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + 3 a^{2} - 9 a - 1\) , \( -4 a^{3} + a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(a^{3}+3a^{2}-9a-1\right){x}-4a^{3}+a^{2}+10a+2$ |
| 145.3-e1 |
145.3-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$40.03147792$ |
1.193508078 |
\( -\frac{139663094425313345658125359}{145} a^{3} + \frac{412885335871671877657434893}{145} a^{2} - \frac{249073223620841475224327887}{145} a - \frac{71391625517732449724526609}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -791 a^{3} + 688 a^{2} + 3761 a - 4369\) , \( -28142 a^{3} + 39690 a^{2} + 87295 a - 120457\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-791a^{3}+688a^{2}+3761a-4369\right){x}-28142a^{3}+39690a^{2}+87295a-120457$ |
| 145.3-e2 |
145.3-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$160.1259116$ |
1.193508078 |
\( -\frac{823667747796206}{4205} a^{3} + \frac{2664464498192138}{4205} a^{2} - \frac{1728023804760081}{4205} a - \frac{97046134394625}{841} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -56 a^{3} + 38 a^{2} + 251 a - 269\) , \( -434 a^{3} + 563 a^{2} + 1276 a - 1676\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-56a^{3}+38a^{2}+251a-269\right){x}-434a^{3}+563a^{2}+1276a-1676$ |
| 145.3-e3 |
145.3-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$640.5036467$ |
1.193508078 |
\( -\frac{2933204979116}{145} a^{3} - \frac{992240865343}{145} a^{2} + \frac{10405077677262}{145} a + \frac{2191819495669}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -6 a^{3} + 8 a^{2} + 26 a - 34\) , \( 14 a^{3} - 15 a^{2} - 59 a + 72\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-6a^{3}+8a^{2}+26a-34\right){x}+14a^{3}-15a^{2}-59a+72$ |
| 145.3-e4 |
145.3-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.00786948$ |
1.193508078 |
\( \frac{554067534321934638207193583}{707281} a^{3} + \frac{2291321120460720703238799999}{3536405} a^{2} - \frac{1378979736648760870757309297}{707281} a - \frac{1516256059527960008257577563}{3536405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -121 a^{3} - 132 a^{2} + 341 a + 71\) , \( -2518 a^{3} + 448 a^{2} + 7457 a - 4747\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-121a^{3}-132a^{2}+341a+71\right){x}-2518a^{3}+448a^{2}+7457a-4747$ |
| 145.3-f1 |
145.3-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( -\frac{139663094425313345658125359}{145} a^{3} + \frac{412885335871671877657434893}{145} a^{2} - \frac{249073223620841475224327887}{145} a - \frac{71391625517732449724526609}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -2 a^{3} - 188 a^{2} + 310 a - 79\) , \( 1231 a^{3} - 2720 a^{2} + 732 a + 947\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-2a^{3}-188a^{2}+310a-79\right){x}+1231a^{3}-2720a^{2}+732a+947$ |
| 145.3-f2 |
145.3-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( -\frac{2933204979116}{145} a^{3} - \frac{992240865343}{145} a^{2} + \frac{10405077677262}{145} a + \frac{2191819495669}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -2 a^{3} - 3 a^{2} + 5 a + 1\) , \( 4 a^{3} + 2 a^{2} - 10 a - 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-2a^{3}-3a^{2}+5a+1\right){x}+4a^{3}+2a^{2}-10a-3$ |
| 145.3-f3 |
145.3-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( -\frac{823667747796206}{4205} a^{3} + \frac{2664464498192138}{4205} a^{2} - \frac{1728023804760081}{4205} a - \frac{97046134394625}{841} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -37 a^{3} - 43 a^{2} + 110 a + 16\) , \( 207 a^{3} + 112 a^{2} - 455 a - 91\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-37a^{3}-43a^{2}+110a+16\right){x}+207a^{3}+112a^{2}-455a-91$ |
| 145.3-f4 |
145.3-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( \frac{554067534321934638207193583}{707281} a^{3} + \frac{2291321120460720703238799999}{3536405} a^{2} - \frac{1378979736648760870757309297}{707281} a - \frac{1516256059527960008257577563}{3536405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -632 a^{3} - 538 a^{2} + 1590 a + 351\) , \( 12035 a^{3} + 9884 a^{2} - 29902 a - 6541\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-632a^{3}-538a^{2}+1590a+351\right){x}+12035a^{3}+9884a^{2}-29902a-6541$ |
*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.
