| 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 |
| 9.2-a1 |
9.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.945878584$ |
2.600289635 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -38 a + 99\) , \( 38 a + 673\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(-38a+99\right){x}+38a+673$ |
| 9.2-a2 |
9.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.729392922$ |
2.600289635 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 2 a - 1\) , \( -a + 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(2a-1\right){x}-a+1$ |
| 9.2-a3 |
9.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{14} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 1 \) |
$1$ |
$9.729392922$ |
2.600289635 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 3 a + 2\) , \( -3 a - 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(3a+2\right){x}-3a-1$ |
| 9.2-a4 |
9.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{22} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 5 \) |
$1$ |
$1.945878584$ |
2.600289635 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 163 a + 402\) , \( -468 a + 7949\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(163a+402\right){x}-468a+7949$ |
| 9.2-b1 |
9.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.945878584$ |
2.600289635 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 37 a + 99\) , \( -38 a + 673\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(37a+99\right){x}-38a+673$ |
| 9.2-b2 |
9.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.729392922$ |
2.600289635 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -3 a - 1\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(-3a-1\right){x}+a+1$ |
| 9.2-b3 |
9.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{14} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 1 \) |
$1$ |
$9.729392922$ |
2.600289635 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -4 a + 2\) , \( 3 a - 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-4a+2\right){x}+3a-1$ |
| 9.2-b4 |
9.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 3^{22} \) |
$1.15823$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 5 \) |
$1$ |
$1.945878584$ |
2.600289635 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -164 a + 402\) , \( 468 a + 7949\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-164a+402\right){x}+468a+7949$ |
| 14.1-a1 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.875417135$ |
0.233965070 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 14.1-a2 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$7.878754216$ |
0.233965070 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 14.1-a3 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
0.233965070 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 14.1-a4 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.233965070 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 14.1-a5 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$3.939377108$ |
0.233965070 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 14.1-a6 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.437708567$ |
0.233965070 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 14.1-b1 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{48} \cdot 7^{2} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$0.875417135$ |
2.105685636 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -673\) , \( -6305\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-673{x}-6305$ |
| 14.1-b2 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.878754216$ |
2.105685636 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 7\) , \( 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+7{x}+7$ |
| 14.1-b3 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{24} \cdot 7^{6} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.626251405$ |
2.105685636 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 27\) , \( -61\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+27{x}-61$ |
| 14.1-b4 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{12} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.313125702$ |
2.105685636 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -133\) , \( -413\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-133{x}-413$ |
| 14.1-b5 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{14} \cdot 7^{4} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.939377108$ |
2.105685636 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -33\) , \( 143\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-33{x}+143$ |
| 14.1-b6 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{30} \cdot 7^{4} \) |
$1.29349$ |
$(2,a), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{3} \) |
$1$ |
$0.437708567$ |
2.105685636 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -10913\) , \( -430241\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-10913{x}-430241$ |
| 27.2-a1 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{28} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( -\frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -53 a - 125\) , \( 459 a + 407\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-53a-125\right){x}+459a+407$ |
| 27.2-a2 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{16} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( \frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 3 a - 16\) , \( 3 a - 13\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(3a-16\right){x}+3a-13$ |
| 27.2-a3 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( -\frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 26\) , \( 14 a + 8\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(4a-26\right){x}+14a+8$ |
| 27.2-a4 |
27.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( \frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -12 a + 44\) , \( 100 a - 62\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(-12a+44\right){x}+100a-62$ |
| 27.2-b1 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{28} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \) |
$0.506563766$ |
$2.224443012$ |
2.409247270 |
\( -\frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -13 a + 239\) , \( 296 a + 218\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-13a+239\right){x}+296a+218$ |
| 27.2-b2 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.039382599$ |
$2.224443012$ |
2.409247270 |
\( \frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24 a - 66\) , \( 126 a + 72\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(24a-66\right){x}+126a+72$ |
| 27.2-b3 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{20} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.519691299$ |
$2.224443012$ |
2.409247270 |
\( -\frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( 3 a + 19\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(2a-1\right){x}+3a+19$ |
| 27.2-b4 |
27.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1.013127533$ |
$2.224443012$ |
2.409247270 |
\( \frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -8 a - 35\) , \( 80 a - 36\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-8a-35\right){x}+80a-36$ |
| 27.3-a1 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{16} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( -\frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4 a - 16\) , \( -3 a - 13\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(-4a-16\right){x}-3a-13$ |
| 27.3-a2 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{28} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( \frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 52 a - 125\) , \( -460 a + 407\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(52a-125\right){x}-460a+407$ |
| 27.3-a3 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( -\frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 11 a + 44\) , \( -100 a - 62\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(11a+44\right){x}-100a-62$ |
| 27.3-a4 |
27.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.224443012$ |
1.189014804 |
\( \frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 26\) , \( -14 a + 8\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-4a-26\right){x}-14a+8$ |
| 27.3-b1 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.039382599$ |
$2.224443012$ |
2.409247270 |
\( -\frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -24 a - 66\) , \( -126 a + 72\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-24a-66\right){x}-126a+72$ |
| 27.3-b2 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{28} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.506563766$ |
$2.224443012$ |
2.409247270 |
\( \frac{40736000}{729} a - \frac{178168000}{729} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 12 a + 239\) , \( -297 a + 218\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(12a+239\right){x}-297a+218$ |
| 27.3-b3 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.013127533$ |
$2.224443012$ |
2.409247270 |
\( -\frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 7 a - 35\) , \( -81 a - 36\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(7a-35\right){x}-81a-36$ |
| 27.3-b4 |
27.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{20} \) |
$1.52431$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.519691299$ |
$2.224443012$ |
2.409247270 |
\( \frac{35872000}{531441} a + \frac{202568000}{531441} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -3 a - 1\) , \( -4 a + 19\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-3a-1\right){x}-4a+19$ |
| 30.2-a1 |
30.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{18} \cdot 5^{8} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.110539852$ |
1.187217040 |
\( \frac{5368185993335879}{569531250} a - \frac{4935622404653413}{284765625} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -435 a + 866\) , \( 1181 a - 30433\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-435a+866\right){x}+1181a-30433$ |
| 30.2-a2 |
30.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{36} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.110539852$ |
1.187217040 |
\( -\frac{1533137111331847}{14121476824050} a + \frac{505776860216309}{7060738412025} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 55 a + 46\) , \( 97 a - 2613\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(55a+46\right){x}+97a-2613$ |
| 30.2-a3 |
30.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{4} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.221079705$ |
1.187217040 |
\( \frac{469954830037}{332150625} a + \frac{2706524302219}{664301250} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -30 a + 56\) , \( 47 a - 463\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-30a+56\right){x}+47a-463$ |
| 30.2-a4 |
30.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.442159411$ |
1.187217040 |
\( -\frac{30893401}{18225} a + \frac{331866001}{72900} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -10 a + 6\) , \( a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-10a+6\right){x}+a+57$ |
| 30.2-b1 |
30.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{18} \cdot 5^{8} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.110539852$ |
3.561651122 |
\( \frac{5368185993335879}{569531250} a - \frac{4935622404653413}{284765625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 378 a + 1167\) , \( 1895 a - 29621\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(378a+1167\right){x}+1895a-29621$ |
| 30.2-b2 |
30.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{36} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.110539852$ |
3.561651122 |
\( -\frac{1533137111331847}{14121476824050} a + \frac{505776860216309}{7060738412025} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -12 a - 213\) , \( 295 a - 2193\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-12a-213\right){x}+295a-2193$ |
| 30.2-b3 |
30.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{4} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$2.221079705$ |
3.561651122 |
\( \frac{469954830037}{332150625} a + \frac{2706524302219}{664301250} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 23 a + 77\) , \( 15 a - 463\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(23a+77\right){x}+15a-463$ |
| 30.2-b4 |
30.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.2 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+1), (5,a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.442159411$ |
3.561651122 |
\( -\frac{30893401}{18225} a + \frac{331866001}{72900} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 3 a + 27\) , \( -15 a + 29\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(3a+27\right){x}-15a+29$ |
| 30.3-a1 |
30.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{18} \cdot 5^{8} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.110539852$ |
1.187217040 |
\( -\frac{5368185993335879}{569531250} a - \frac{4935622404653413}{284765625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 434 a + 866\) , \( -1181 a - 30433\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(434a+866\right){x}-1181a-30433$ |
| 30.3-a2 |
30.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{36} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.110539852$ |
1.187217040 |
\( \frac{1533137111331847}{14121476824050} a + \frac{505776860216309}{7060738412025} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -56 a + 46\) , \( -97 a - 2613\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-56a+46\right){x}-97a-2613$ |
| 30.3-a3 |
30.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{4} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.221079705$ |
1.187217040 |
\( -\frac{469954830037}{332150625} a + \frac{2706524302219}{664301250} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 29 a + 56\) , \( -47 a - 463\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(29a+56\right){x}-47a-463$ |
| 30.3-a4 |
30.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.442159411$ |
1.187217040 |
\( \frac{30893401}{18225} a + \frac{331866001}{72900} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 9 a + 6\) , \( -a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(9a+6\right){x}-a+57$ |
| 30.3-b1 |
30.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{18} \cdot 5^{8} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.110539852$ |
3.561651122 |
\( -\frac{5368185993335879}{569531250} a - \frac{4935622404653413}{284765625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -379 a + 1167\) , \( -1896 a - 29621\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-379a+1167\right){x}-1896a-29621$ |
| 30.3-b2 |
30.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
30.3 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2 \cdot 3^{36} \cdot 5^{2} \) |
$1.56499$ |
$(2,a), (3,a+2), (5,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.110539852$ |
3.561651122 |
\( \frac{1533137111331847}{14121476824050} a + \frac{505776860216309}{7060738412025} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 11 a - 213\) , \( -296 a - 2193\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(11a-213\right){x}-296a-2193$ |
*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.
