| 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 |
| 8932.5-j1 |
8932.5-j |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8932.5 |
\( 2^{2} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{30} \cdot 7^{5} \cdot 11^{3} \cdot 29 \) |
$2.29840$ |
$(a), (-a+1), (-2a+1), (-2a+3), (-4a+1)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{3} \) |
$0.726269176$ |
$0.450050668$ |
7.412441087 |
\( \frac{8327088487989}{54228815872} a - \frac{172280835539917}{433830526976} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 98 a - 105\) , \( 1188 a - 615\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(98a-105\right){x}+1188a-615$ |
| 8932.8-j1 |
8932.8-j |
$4$ |
$15$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8932.8 |
\( 2^{2} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{30} \cdot 7^{5} \cdot 11^{3} \cdot 29 \) |
$2.29840$ |
$(a), (-a+1), (-2a+1), (2a+1), (4a-3)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{3} \) |
$0.726269176$ |
$0.450050668$ |
7.412441087 |
\( -\frac{8327088487989}{54228815872} a - \frac{105664127636005}{433830526976} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -99 a - 6\) , \( -1189 a + 574\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-99a-6\right){x}-1189a+574$ |
| 100.2-b4 |
100.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 5^{4} \) |
$1.09442$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.2, 5B.1.2 |
$1$ |
\( 3^{3} \cdot 5^{2} \) |
$1$ |
$1.424166746$ |
2.206309637 |
\( \frac{46969655}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+22{x}-9$ |
| 100.1-b2 |
100.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{4} \) |
$0.63186$ |
$(-2a+1), (2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$22.88719308$ |
0.682364260 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 22.1-b3 |
22.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{15} \cdot 11^{3} \) |
$0.67040$ |
$(a+1), (-2a+1)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$14.94742555$ |
0.862990016 |
\( \frac{7452136447}{340736} a - \frac{12920117437}{340736} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 20 a - 32\) , \( -64 a + 112\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-32\right){x}-64a+112$ |
| 22.2-b2 |
22.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{15} \cdot 11^{3} \) |
$0.67040$ |
$(a+1), (2a+1)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$14.94742555$ |
0.862990016 |
\( -\frac{7452136447}{340736} a - \frac{12920117437}{340736} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -20 a - 32\) , \( 64 a + 112\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-32\right){x}+64a+112$ |
| 372.1-d1 |
372.1-d |
$4$ |
$15$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
372.1 |
\( 2^{2} \cdot 3 \cdot 31 \) |
\( 2^{30} \cdot 3^{5} \cdot 31^{3} \) |
$2.25440$ |
$(-a-2), (-a+3), (-2a+7), (-2a-7)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{3} \) |
$1$ |
$2.272867778$ |
5.934832428 |
\( -\frac{4955692963031933}{6589292544} a - \frac{46989724039860695}{26357170176} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -15763 a - 37391\) , \( 1847753 a + 4383391\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15763a-37391\right){x}+1847753a+4383391$ |
| 372.2-d4 |
372.2-d |
$4$ |
$15$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
372.2 |
\( 2^{2} \cdot 3 \cdot 31 \) |
\( 2^{30} \cdot 3^{5} \cdot 31^{3} \) |
$2.25440$ |
$(-a-2), (-a+3), (-2a+7), (-2a+9)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{3} \) |
$1$ |
$2.272867778$ |
5.934832428 |
\( \frac{4955692963031933}{6589292544} a - \frac{66812495891988427}{26357170176} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 15764 a - 53154\) , \( -1831991 a + 6177991\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(15764a-53154\right){x}-1831991a+6177991$ |
| 400.1-b3 |
400.1-b |
$4$ |
$15$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{4} \) |
$6.33829$ |
$(-a-1), (2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1272.252497$ |
1.517249636 |
\( -\frac{349938025}{8} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( 25 a^{3} - 75 a - 25\) , \( -103 a^{3} + 309 a + 71\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(25a^{3}-75a-25\right){x}-103a^{3}+309a+71$ |
| 400.1-c1 |
400.1-c |
$4$ |
$15$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$6.33829$ |
$(-a-1), (2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$523.8236072$ |
1.041160172 |
\( -\frac{121945}{32} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{3} - 3 a + 1\) , \( -3 a^{2} - 13 a - 11\) , \( a^{3} + 10 a^{2} + 27 a + 21\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{2}-13a-11\right){x}+a^{3}+10a^{2}+27a+21$ |
| 100.1-a3 |
100.1-a |
$4$ |
$15$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$7.10646$ |
$(a), (a^3-a^2-3a+2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$523.8236072$ |
1.561740258 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 242.1-b1 |
242.1-b |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$8.51837$ |
$(a^3-4a+1), (-2a^2+5)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$223.4255307$ |
1.861879423 |
\( \frac{7452136447}{340736} a^{2} - \frac{27824390331}{340736} \) |
\( \bigl[a\) , \( -1\) , \( a^{3} - 4 a\) , \( -4\) , \( 6 a^{2} + 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}-4{x}+6a^{2}+3$ |
| 242.2-b4 |
242.2-b |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
242.2 |
\( 2 \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$8.51837$ |
$(a^3-4a+1), (-2a^2+3)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$223.4255307$ |
1.861879423 |
\( -\frac{7452136447}{340736} a^{2} + \frac{1984155457}{340736} \) |
\( \bigl[a^{3} - 4 a\) , \( -1\) , \( a\) , \( -4\) , \( -6 a^{2} + 27\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+a{y}={x}^{3}-{x}^{2}-4{x}-6a^{2}+27$ |
| 484.2-f2 |
484.2-f |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$11.61169$ |
$(-1/7a^3+5/7a^2-1/7a-19/7), (-1/7a^3+5/7a^2+13/7a-5/7), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3^{3} \cdot 5 \) |
$0.385176290$ |
$223.4255307$ |
3.442328685 |
\( \frac{1064590921}{170368} a^{3} - \frac{3193772763}{340736} a^{2} - \frac{20227227499}{340736} a - \frac{2274208227}{340736} \) |
\( \bigl[1\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{19}{7} a + \frac{17}{7}\) , \( 0\) , \( \frac{40}{7} a^{3} - \frac{60}{7} a^{2} - \frac{380}{7} a - \frac{24}{7}\) , \( -\frac{128}{7} a^{3} + \frac{192}{7} a^{2} + \frac{1216}{7} a + \frac{144}{7}\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{19}{7}a+\frac{17}{7}\right){x}^{2}+\left(\frac{40}{7}a^{3}-\frac{60}{7}a^{2}-\frac{380}{7}a-\frac{24}{7}\right){x}-\frac{128}{7}a^{3}+\frac{192}{7}a^{2}+\frac{1216}{7}a+\frac{144}{7}$ |
| 484.6-f2 |
484.6-f |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
484.6 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$11.61169$ |
$(-a-1), (a-3), (-2/7a^3+3/7a^2+19/7a-3/7)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3^{3} \cdot 5 \) |
$0.385176290$ |
$223.4255307$ |
3.442328685 |
\( -\frac{1064590921}{170368} a^{3} + \frac{3193772763}{340736} a^{2} + \frac{20227227499}{340736} a - \frac{23566026647}{340736} \) |
\( \bigl[1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( 0\) , \( -\frac{40}{7} a^{3} + \frac{60}{7} a^{2} + \frac{380}{7} a - \frac{424}{7}\) , \( \frac{128}{7} a^{3} - \frac{192}{7} a^{2} - \frac{1216}{7} a + \frac{1424}{7}\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}^{2}+\left(-\frac{40}{7}a^{3}+\frac{60}{7}a^{2}+\frac{380}{7}a-\frac{424}{7}\right){x}+\frac{128}{7}a^{3}-\frac{192}{7}a^{2}-\frac{1216}{7}a+\frac{1424}{7}$ |
| 44.1-a2 |
44.1-a |
$4$ |
$15$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{30} \cdot 11^{6} \) |
$9.88572$ |
$(a^2-2a-2), (a^2-a-1)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$223.4255307$ |
1.296446422 |
\( \frac{7452136447}{340736} a^{2} - \frac{7452136447}{340736} a - \frac{27824390331}{340736} \) |
\( \bigl[1\) , \( a^{2} - a - 1\) , \( 0\) , \( 20 a^{2} - 20 a - 72\) , \( -64 a^{2} + 64 a + 240\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(20a^{2}-20a-72\right){x}-64a^{2}+64a+240$ |
| 484.2-f4 |
484.2-f |
$4$ |
$15$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$13.34082$ |
$(a^2-a-1), (2a^2-2a-3)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$223.4255307$ |
0.648223211 |
\( -\frac{7452136447}{340736} a^{2} + \frac{7452136447}{340736} a + \frac{1984155457}{340736} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( 0\) , \( -20 a^{2} + 20 a + 8\) , \( 64 a^{2} - 64 a - 16\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-20a^{2}+20a+8\right){x}+64a^{2}-64a-16$ |
| 400.1-h3 |
400.1-h |
$4$ |
$15$ |
4.4.5125.1 |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$13.52829$ |
$(-a^3+a^2+4a+1), (2)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$523.8236072$ |
0.487805702 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 242.1-e2 |
242.1-e |
$4$ |
$15$ |
4.4.7488.1 |
$4$ |
$[4, 0]$ |
242.1 |
\( 2 \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$15.35672$ |
$(a+1), (2a^3-4a^2-6a+3)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$1$ |
$223.4255307$ |
1.032784881 |
\( -\frac{7452136447}{340736} a^{3} + \frac{7452136447}{170368} a^{2} + \frac{22356409341}{340736} a - \frac{5093063471}{85184} \) |
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( 0\) , \( -20 a^{3} + 40 a^{2} + 60 a - 52\) , \( 64 a^{3} - 128 a^{2} - 192 a + 176\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(-20a^{3}+40a^{2}+60a-52\right){x}+64a^{3}-128a^{2}-192a+176$ |
| 242.2-a2 |
242.2-a |
$4$ |
$15$ |
4.4.7488.1 |
$4$ |
$[4, 0]$ |
242.2 |
\( 2 \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{6} \) |
$15.35672$ |
$(a+1), (-a^3+2a^2+4a), (-a+2)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5 \) |
$0.495052724$ |
$223.4255307$ |
6.135395629 |
\( \frac{7452136447}{340736} a^{3} - \frac{7452136447}{170368} a^{2} - \frac{22356409341}{340736} a - \frac{2733990495}{170368} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( 20 a^{3} - 40 a^{2} - 60 a - 12\) , \( -64 a^{3} + 128 a^{2} + 192 a + 48\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(20a^{3}-40a^{2}-60a-12\right){x}-64a^{3}+128a^{2}+192a+48$ |
| 100.1-g2 |
100.1-g |
$4$ |
$15$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$14.21293$ |
$(1/2a^3+1/2a^2-3a-5), (a^2+a-4)$ |
0 |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 5$ |
3B.1.1, 5B.1.1[2] |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$523.8236072$ |
0.780870129 |
\( -\frac{121945}{32} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 44.2-f2 |
44.2-f |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{30} \cdot 11^{6} \) |
$18.92971$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a), (1/2a^3+a^2-7/2a-6)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
$0.220454762$ |
$223.4255307$ |
8.955494977 |
\( -\frac{7452136447}{681472} a^{3} + \frac{37260682235}{681472} a - \frac{12920117437}{340736} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 1\) , \( 0\) , \( -10 a^{3} + 50 a - 32\) , \( 32 a^{3} - 160 a + 112\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+1\right){x}^{2}+\left(-10a^{3}+50a-32\right){x}+32a^{3}-160a+112$ |
| 44.5-f2 |
44.5-f |
$4$ |
$15$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
44.5 |
\( 2^{2} \cdot 11 \) |
\( 2^{30} \cdot 11^{6} \) |
$18.92971$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a), (a^3+a^2-6a-7)$ |
$1$ |
$\Z/15\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
$0.220454762$ |
$223.4255307$ |
8.955494977 |
\( \frac{7452136447}{681472} a^{3} - \frac{37260682235}{681472} a - \frac{12920117437}{340736} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( 0\) , \( 10 a^{3} - 50 a - 32\) , \( -32 a^{3} + 160 a + 112\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}^{2}+\left(10a^{3}-50a-32\right){x}-32a^{3}+160a+112$ |
*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.
