| 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 |
| 12.1-a1 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$1.60389$ |
$(a+4), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$10.71379314$ |
2.221937192 |
\( -\frac{644509}{24} a - \frac{3327686}{27} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -2 a\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-2a{x}+2$ |
| 12.1-a2 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.60389$ |
$(a+4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.190421460$ |
2.221937192 |
\( \frac{3280045171285}{64} a - \frac{418939862638603}{1536} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 13 a\) , \( 72 a + 8\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+13a{x}+72a+8$ |
| 12.1-b1 |
12.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$1.60389$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.230662920$ |
$7.696166126$ |
2.208981058 |
\( -\frac{644509}{24} a - \frac{3327686}{27} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 68 a - 356\) , \( -649 a + 3442\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(68a-356\right){x}-649a+3442$ |
| 12.1-b2 |
12.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.60389$ |
$(a+4), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.691988761$ |
$7.696166126$ |
2.208981058 |
\( \frac{3280045171285}{64} a - \frac{418939862638603}{1536} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 4794 a + 20735\) , \( -616277 a - 2663425\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4794a+20735\right){x}-616277a-2663425$ |
| 12.1-c1 |
12.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.60389$ |
$(a+4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.190421460$ |
2.221937192 |
\( -\frac{3280045171285}{64} a - \frac{340218778527763}{1536} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -14 a + 13\) , \( -72 a + 80\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-14a+13\right){x}-72a+80$ |
| 12.1-c2 |
12.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$1.60389$ |
$(a+4), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$10.71379314$ |
2.221937192 |
\( \frac{644509}{24} a - \frac{32422069}{216} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( a - 2\) , \( 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-2\right){x}+2$ |
| 12.1-d1 |
12.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.60389$ |
$(a+4), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.691988761$ |
$7.696166126$ |
2.208981058 |
\( -\frac{3280045171285}{64} a - \frac{340218778527763}{1536} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -4796 a + 25531\) , \( 616276 a - 3279701\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-4796a+25531\right){x}+616276a-3279701$ |
| 12.1-d2 |
12.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{6} \cdot 3^{6} \) |
$1.60389$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.230662920$ |
$7.696166126$ |
2.208981058 |
\( \frac{644509}{24} a - \frac{32422069}{216} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -69 a - 288\) , \( 648 a + 2793\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-69a-288\right){x}+648a+2793$ |
| 16.1-a1 |
16.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.834889332 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 8\) , \( 89 a - 483\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+8\right){x}+89a-483$ |
| 16.1-a2 |
16.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.834889332 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 8\) , \( a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+8\right){x}+a+3$ |
| 16.1-b1 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 31$ |
2B, 31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.458722333 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 8\) , \( 2 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+8\right){x}+2a+10$ |
| 16.1-b2 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2, 31$ |
2B, 31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.458722333 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 8\) , \( -2 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+8\right){x}-2a+20$ |
| 16.1-b3 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.72349$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.458722333 |
\( 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a - 57\) , \( 99 a + 429\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a-57\right){x}+99a+429$ |
| 16.1-b4 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.72349$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
0.458722333 |
\( 54000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a - 72\) , \( -84 a + 456\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-72\right){x}-84a+456$ |
| 16.1-c1 |
16.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.834889332 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 8\) , \( -a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+8\right){x}-a-4$ |
| 16.1-c2 |
16.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.72349$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$31$ |
31Ns.7.1 |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.834889332 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 8\) , \( -89 a - 386\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+8\right){x}-89a-386$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.525348743$ |
$11.08189506$ |
3.622192333 |
\( -243 a + 756 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a + 18\) , \( -3 a + 16\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+18\right){x}-3a+16$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.576046229$ |
$11.08189506$ |
3.622192333 |
\( -46788681 a + 249001629 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 40 a + 178\) , \( 604 a + 2614\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a+178\right){x}+604a+2614$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$3.125160028$ |
$42.90936195$ |
3.090084315 |
\( -243 a + 756 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 8\) , \( 6 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-8\right){x}+6a-5$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1.041720009$ |
$4.767706883$ |
3.090084315 |
\( -46788681 a + 249001629 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 144 a - 753\) , \( 2163 a - 11484\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(144a-753\right){x}+2163a-11484$ |
| 27.1-c1 |
27.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.525348743$ |
$11.08189506$ |
3.622192333 |
\( 243 a + 513 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a + 15\) , \( 3 a + 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a+15\right){x}+3a+13$ |
| 27.1-c2 |
27.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.576046229$ |
$11.08189506$ |
3.622192333 |
\( 46788681 a + 202212948 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -42 a + 219\) , \( -605 a + 3218\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-42a+219\right){x}-605a+3218$ |
| 27.1-d1 |
27.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$3.125160028$ |
$42.90936195$ |
3.090084315 |
\( 243 a + 513 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -6 a - 2\) , \( -7 a + 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-2\right){x}-7a+2$ |
| 27.1-d2 |
27.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1.041720009$ |
$4.767706883$ |
3.090084315 |
\( 46788681 a + 202212948 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -146 a - 607\) , \( -2164 a - 9320\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-146a-607\right){x}-2164a-9320$ |
| 27.1-e1 |
27.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$26.19039539$ |
2.715817489 |
\( 243 a + 513 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 40 a - 213\) , \( -567 a + 3018\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a-213\right){x}-567a+3018$ |
| 27.1-e2 |
27.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$26.19039539$ |
2.715817489 |
\( 46788681 a + 202212948 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 10\) , \( -a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-10\right){x}-a+2$ |
| 27.1-f1 |
27.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$20.29202021$ |
2.104184475 |
\( 243 a + 513 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -3\) , \( -10\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-3{x}-10$ |
| 27.1-f2 |
27.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$20.29202021$ |
2.104184475 |
\( 46788681 a + 202212948 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 22\) , \( -18 a + 87\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a+22\right){x}-18a+87$ |
| 27.1-g1 |
27.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$26.19039539$ |
2.715817489 |
\( -243 a + 756 \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -41 a - 173\) , \( 567 a + 2451\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-41a-173\right){x}+567a+2451$ |
| 27.1-g2 |
27.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$26.19039539$ |
2.715817489 |
\( -46788681 a + 249001629 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 2 a - 12\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2a-12\right){x}+2$ |
| 27.1-h1 |
27.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$20.29202021$ |
2.104184475 |
\( -243 a + 756 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a - 2\) , \( -a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-2\right){x}-a-9$ |
| 27.1-h2 |
27.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$1.96436$ |
$(a+4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$20.29202021$ |
2.104184475 |
\( -46788681 a + 249001629 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a + 18\) , \( 17 a + 70\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a+18\right){x}+17a+70$ |
| 28.1-a1 |
28.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{5} \) |
$1.98230$ |
$(-a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.441450826$ |
$6.991270514$ |
3.200346245 |
\( -\frac{21412661}{134456} a - \frac{45409017}{67228} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -21 a - 87\) , \( -135 a - 582\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-21a-87\right){x}-135a-582$ |
| 28.1-a2 |
28.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$1.98230$ |
$(-a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$2.207254134$ |
$6.991270514$ |
3.200346245 |
\( \frac{2143178584772231}{229376} a - \frac{11405622218781845}{229376} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -261 a - 1132\) , \( 19307 a + 83442\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-261a-1132\right){x}+19307a+83442$ |
| 28.1-b1 |
28.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{5} \) |
$1.98230$ |
$(-a+6), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$4.966742900$ |
$10.65365922$ |
2.194769910 |
\( -\frac{21412661}{134456} a - \frac{45409017}{67228} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 6 a + 26\) , \( 18 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a+26\right){x}+18a+26$ |
| 28.1-b2 |
28.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$1.98230$ |
$(-a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$24.83371450$ |
$0.426146368$ |
2.194769910 |
\( \frac{2143178584772231}{229376} a - \frac{11405622218781845}{229376} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 681 a - 3569\) , \( 20611 a - 109588\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(681a-3569\right){x}+20611a-109588$ |
| 28.2-a1 |
28.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$1.98230$ |
$(a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$2.207254134$ |
$6.991270514$ |
3.200346245 |
\( -\frac{2143178584772231}{229376} a - \frac{4631221817004807}{114688} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 263 a - 1393\) , \( -19045 a + 101356\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(263a-1393\right){x}-19045a+101356$ |
| 28.2-a2 |
28.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{5} \) |
$1.98230$ |
$(a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.441450826$ |
$6.991270514$ |
3.200346245 |
\( \frac{21412661}{134456} a - \frac{112230695}{134456} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 23 a - 108\) , \( 157 a - 825\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(23a-108\right){x}+157a-825$ |
| 28.2-b1 |
28.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{30} \cdot 7 \) |
$1.98230$ |
$(a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$24.83371450$ |
$0.426146368$ |
2.194769910 |
\( -\frac{2143178584772231}{229376} a - \frac{4631221817004807}{114688} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -671 a - 2910\) , \( -23511 a - 101620\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-671a-2910\right){x}-23511a-101620$ |
| 28.2-b2 |
28.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{5} \) |
$1.98230$ |
$(a+5), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$4.966742900$ |
$10.65365922$ |
2.194769910 |
\( \frac{21412661}{134456} a - \frac{112230695}{134456} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 4 a + 10\) , \( 2 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+10\right){x}+2a+6$ |
| 33.1-a1 |
33.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$2.06542$ |
$(a+4), (a-4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$26.17593247$ |
2.714317754 |
\( \frac{618496372412416}{33} a - \frac{3291530565128192}{33} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 51 a - 306\) , \( -566 a + 3045\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(51a-306\right){x}-566a+3045$ |
| 33.1-a2 |
33.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11^{3} \) |
$2.06542$ |
$(a+4), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$26.17593247$ |
2.714317754 |
\( \frac{69308416}{11979} a - \frac{368881664}{11979} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( a + 4\) , \( -a + 4\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(a+4\right){x}-a+4$ |
| 33.1-b1 |
33.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$2.06542$ |
$(a+4), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$0.460467327$ |
3.867607239 |
\( \frac{618496372412416}{33} a - \frac{3291530565128192}{33} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -3830 a - 16547\) , \( -276573 a - 1195303\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-3830a-16547\right){x}-276573a-1195303$ |
| 33.1-b2 |
33.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11^{3} \) |
$2.06542$ |
$(a+4), (a-4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3^{2} \) |
$1$ |
$4.144205944$ |
3.867607239 |
\( \frac{69308416}{11979} a - \frac{368881664}{11979} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -10 a - 37\) , \( -958 a - 4142\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-10a-37\right){x}-958a-4142$ |
| 33.2-a1 |
33.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$2.06542$ |
$(a+4), (a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$26.17593247$ |
2.714317754 |
\( -\frac{618496372412416}{33} a - \frac{2673034192715776}{33} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -51 a - 255\) , \( 565 a + 2479\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a-255\right){x}+565a+2479$ |
| 33.2-a2 |
33.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11^{3} \) |
$2.06542$ |
$(a+4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$26.17593247$ |
2.714317754 |
\( -\frac{69308416}{11979} a - \frac{299573248}{11979} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -a + 5\) , \( 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+5\right){x}+3$ |
| 33.2-b1 |
33.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$2.06542$ |
$(a+4), (a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$0.460467327$ |
3.867607239 |
\( -\frac{618496372412416}{33} a - \frac{2673034192715776}{33} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 3830 a - 20377\) , \( 276572 a - 1471876\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3830a-20377\right){x}+276572a-1471876$ |
| 33.2-b2 |
33.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( 3^{3} \cdot 11^{3} \) |
$2.06542$ |
$(a+4), (a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3^{2} \) |
$1$ |
$4.144205944$ |
3.867607239 |
\( -\frac{69308416}{11979} a - \frac{299573248}{11979} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 10 a - 47\) , \( 957 a - 5100\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-47\right){x}+957a-5100$ |
| 36.1-a1 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.11084$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.190558319$ |
$17.67209760$ |
2.793601964 |
\( -\frac{644509}{24} a - \frac{3327686}{27} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 16 a + 1\) , \( -11 a + 207\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+1\right){x}-11a+207$ |
| 36.1-a2 |
36.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.11084$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.571674957$ |
$5.890699201$ |
2.793601964 |
\( \frac{3280045171285}{64} a - \frac{418939862638603}{1536} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 601 a - 3104\) , \( -17273 a + 92124\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(601a-3104\right){x}-17273a+92124$ |
*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.
