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 |
1458.1-a1 |
1458.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$4.498619549$ |
1.298639604 |
\( -\frac{413811}{256} a + \frac{624843}{256} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -18 a - 33\) , \( -138 a - 240\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-18a-33\right){x}-138a-240$ |
1458.1-a2 |
1458.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$13.49585864$ |
1.298639604 |
\( -\frac{3063825}{8} a + \frac{5309199}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 18 a + 30\) , \( 108 a + 188\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(18a+30\right){x}+108a+188$ |
1458.1-b1 |
1458.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$35.26759953$ |
3.393626347 |
\( \frac{21249}{4} a - \frac{4887}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a - 3\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-3\right){x}-2a+3$ |
1458.1-b2 |
1458.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$11.75586651$ |
3.393626347 |
\( \frac{355779}{2} a + \frac{619677}{2} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -2 a\) , \( -a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-2a{x}-a-1$ |
1458.1-c1 |
1458.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.259974236$ |
$5.030978620$ |
2.265392252 |
\( -\frac{2110491}{4} a + \frac{3648717}{4} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -5 a - 9\) , \( -12 a - 22\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-5a-9\right){x}-12a-22$ |
1458.1-c2 |
1458.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.779922710$ |
$15.09293586$ |
2.265392252 |
\( -\frac{2025}{2} a + \frac{5481}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a + 7\) , \( 4 a + 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a+7\right){x}+4a+7$ |
1458.1-d1 |
1458.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$9.509784826$ |
2.745238414 |
\( \frac{2025}{2} a + \frac{5481}{2} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -5 a + 6\) , \( 4 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a+6\right){x}+4a-9$ |
1458.1-d2 |
1458.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$28.52935447$ |
2.745238414 |
\( \frac{2110491}{4} a + \frac{3648717}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 9\) , \( -12 a + 21\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-9\right){x}-12a+21$ |
1458.1-e1 |
1458.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \cdot 5 \) |
$0.111398447$ |
$13.04876105$ |
4.196215610 |
\( \frac{413811}{256} a + \frac{624843}{256} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 18 a - 32\) , \( -138 a + 239\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(18a-32\right){x}-138a+239$ |
1458.1-e2 |
1458.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$0.334195343$ |
$4.349587019$ |
4.196215610 |
\( \frac{3063825}{8} a + \frac{5309199}{8} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -18 a + 30\) , \( 108 a - 188\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-18a+30\right){x}+108a-188$ |
1458.1-f1 |
1458.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.607257452$ |
$29.66600381$ |
2.311312993 |
\( \frac{68980869}{4} a - \frac{59741523}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a - 12\) , \( 20 a + 36\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-6a-12\right){x}+20a+36$ |
1458.1-f2 |
1458.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.202419150$ |
$9.888667937$ |
2.311312993 |
\( \frac{14931}{64} a + \frac{12177}{32} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 6 a + 9\) , \( -10 a - 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(6a+9\right){x}-10a-18$ |
1458.1-g1 |
1458.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.466376693$ |
$8.409604824$ |
2.264392979 |
\( -\frac{21249}{4} a - \frac{4887}{4} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -2 a - 3\) , \( -2 a - 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-2a-3\right){x}-2a-4$ |
1458.1-g2 |
1458.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.399130079$ |
$25.22881447$ |
2.264392979 |
\( -\frac{355779}{2} a + \frac{619677}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a + 1\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a+1\right){x}-a-1$ |
1458.1-h1 |
1458.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.179841030$ |
2.517063610 |
\( -\frac{68980869}{4} a - \frac{59741523}{2} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 6 a - 12\) , \( 20 a - 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(6a-12\right){x}+20a-36$ |
1458.1-h2 |
1458.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.539523090$ |
2.517063610 |
\( -\frac{14931}{64} a + \frac{12177}{32} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 10\) , \( -10 a + 17\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+10\right){x}-10a+17$ |
1458.1-i1 |
1458.1-i |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.843795817$ |
1.509539208 |
\( -\frac{189613868625}{128} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 60322 a - 104487\) , \( -10598940 a + 18357906\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(60322a-104487\right){x}-10598940a+18357906$ |
1458.1-i2 |
1458.1-i |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B |
$1$ |
\( 2 \) |
$1$ |
$2.614598605$ |
1.509539208 |
\( -\frac{140625}{8} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-6{x}-6$ |
1458.1-i3 |
1458.1-i |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{42} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B |
$1$ |
\( 2 \) |
$1$ |
$2.614598605$ |
1.509539208 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5302 a - 9185\) , \( -563243 a + 975564\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5302a-9185\right){x}-563243a+975564$ |
1458.1-i4 |
1458.1-i |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.843795817$ |
1.509539208 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3{x}-1$ |
1458.1-j1 |
1458.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$3.756371729$ |
3.253113343 |
\( \frac{180313857}{4} a - \frac{312277113}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 11\) , \( 5 a - 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-11\right){x}+5a-12$ |
1458.1-j2 |
1458.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$11.26911518$ |
3.253113343 |
\( \frac{4766283}{32} a + \frac{8252523}{32} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( 4 a + 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-3a-6\right){x}+4a+5$ |
1458.1-k1 |
1458.1-k |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.262304011$ |
2.612283659 |
\( -\frac{35937}{4} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -6\) , \( -8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-6{x}-8$ |
1458.1-k2 |
1458.1-k |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.786912033$ |
2.612283659 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$ |
1458.1-l1 |
1458.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$3.756371729$ |
3.253113343 |
\( -\frac{180313857}{4} a - \frac{312277113}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 11\) , \( -5 a - 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a-11\right){x}-5a-12$ |
1458.1-l2 |
1458.1-l |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$11.26911518$ |
3.253113343 |
\( -\frac{4766283}{32} a + \frac{8252523}{32} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3 a - 6\) , \( -4 a + 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(3a-6\right){x}-4a+5$ |
1458.1-m1 |
1458.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.062413899$ |
$32.33027387$ |
2.203433717 |
\( -\frac{180313857}{4} a - \frac{312277113}{4} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -3 a - 12\) , \( 5 a + 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-3a-12\right){x}+5a+11$ |
1458.1-m2 |
1458.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.354137966$ |
$10.77675795$ |
2.203433717 |
\( -\frac{4766283}{32} a + \frac{8252523}{32} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a - 6\) , \( 4 a - 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a-6\right){x}+4a-5$ |
1458.1-n1 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.305934883$ |
$19.31991708$ |
2.275005083 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
1458.1-n2 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.101978294$ |
$6.439972360$ |
2.275005083 |
\( \frac{109503}{64} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}$ |
1458.1-o1 |
1458.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.062413899$ |
$32.33027387$ |
2.203433717 |
\( \frac{180313857}{4} a - \frac{312277113}{4} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3 a - 12\) , \( -5 a + 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(3a-12\right){x}-5a+11$ |
1458.1-o2 |
1458.1-o |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{9} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.354137966$ |
$10.77675795$ |
2.203433717 |
\( \frac{4766283}{32} a + \frac{8252523}{32} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a - 6\) , \( -4 a - 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a-6\right){x}-4a-5$ |
1458.1-p1 |
1458.1-p |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B.2.3 |
$1$ |
\( 2 \cdot 7 \) |
$3.080173468$ |
$0.173617472$ |
4.322510075 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 60322 a - 104487\) , \( 10598940 a - 18357907\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(60322a-104487\right){x}+10598940a-18357907$ |
1458.1-p2 |
1458.1-p |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.146674927$ |
$25.52176850$ |
4.322510075 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
1458.1-p3 |
1458.1-p |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{42} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.3 |
$1$ |
\( 2 \cdot 3^{2} \cdot 7 \) |
$1.026724489$ |
$0.520852418$ |
4.322510075 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5302 a - 9186\) , \( 563242 a - 975566\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(5302a-9186\right){x}+563242a-975566$ |
1458.1-p4 |
1458.1-p |
$4$ |
$21$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B.2.1 |
$1$ |
\( 2 \) |
$0.440024781$ |
$8.507256167$ |
4.322510075 |
\( \frac{3375}{2} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+3{x}+1$ |
1458.1-q1 |
1458.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.607257452$ |
$29.66600381$ |
2.311312993 |
\( -\frac{68980869}{4} a - \frac{59741523}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 6 a - 12\) , \( -20 a + 36\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(6a-12\right){x}-20a+36$ |
1458.1-q2 |
1458.1-q |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.202419150$ |
$9.888667937$ |
2.311312993 |
\( -\frac{14931}{64} a + \frac{12177}{32} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a + 9\) , \( 10 a - 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-6a+9\right){x}+10a-18$ |
1458.1-r1 |
1458.1-r |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$35.26759953$ |
3.393626347 |
\( -\frac{21249}{4} a - \frac{4887}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$ |
1458.1-r2 |
1458.1-r |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$11.75586651$ |
3.393626347 |
\( -\frac{355779}{2} a + \frac{619677}{2} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}-1$ |
1458.1-s1 |
1458.1-s |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.179841030$ |
2.517063610 |
\( \frac{68980869}{4} a - \frac{59741523}{2} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -6 a - 12\) , \( -20 a - 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-6a-12\right){x}-20a-36$ |
1458.1-s2 |
1458.1-s |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.539523090$ |
2.517063610 |
\( \frac{14931}{64} a + \frac{12177}{32} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a + 10\) , \( 10 a + 17\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a+10\right){x}+10a+17$ |
1458.1-t1 |
1458.1-t |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{15} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$4.498619549$ |
1.298639604 |
\( \frac{413811}{256} a + \frac{624843}{256} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 18 a - 33\) , \( 138 a - 240\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(18a-33\right){x}+138a-240$ |
1458.1-t2 |
1458.1-t |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{5} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$13.49585864$ |
1.298639604 |
\( \frac{3063825}{8} a + \frac{5309199}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a + 30\) , \( -108 a + 188\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-18a+30\right){x}-108a+188$ |
1458.1-u1 |
1458.1-u |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.779922710$ |
$15.09293586$ |
2.265392252 |
\( \frac{2025}{2} a + \frac{5481}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 7\) , \( -5 a + 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a+7\right){x}-5a+7$ |
1458.1-u2 |
1458.1-u |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.259974236$ |
$5.030978620$ |
2.265392252 |
\( \frac{2110491}{4} a + \frac{3648717}{4} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 4 a - 9\) , \( 12 a - 22\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(4a-9\right){x}+12a-22$ |
1458.1-v1 |
1458.1-v |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$28.52935447$ |
2.745238414 |
\( -\frac{2110491}{4} a + \frac{3648717}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -5 a - 9\) , \( 12 a + 21\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5a-9\right){x}+12a+21$ |
1458.1-v2 |
1458.1-v |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$9.509784826$ |
2.745238414 |
\( -\frac{2025}{2} a + \frac{5481}{2} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 4 a + 6\) , \( -5 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a+6\right){x}-5a-9$ |
1458.1-w1 |
1458.1-w |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2^{3} \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.466376693$ |
$8.409604824$ |
2.264392979 |
\( \frac{21249}{4} a - \frac{4887}{4} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( a - 3\) , \( 2 a - 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-3\right){x}+2a-4$ |
1458.1-w2 |
1458.1-w |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( - 2 \cdot 3^{6} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.399130079$ |
$25.22881447$ |
2.264392979 |
\( \frac{355779}{2} a + \frac{619677}{2} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a + 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}-1$ |
*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.