| 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 |
| 27.2-a1 |
27.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.85575$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$0.085409766$ |
$2.223297910$ |
2.334447830 |
\( \frac{1295029}{2187} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 10 a + 36\) , \( -72 a - 61\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(10a+36\right){x}-72a-61$ |
| 27.3-a1 |
27.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{32} \) |
$1.85575$ |
$(3,a), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$0.085409766$ |
$2.223297910$ |
2.334447830 |
\( \frac{1295029}{2187} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -11 a + 46\) , \( 72 a - 133\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-11a+46\right){x}+72a-133$ |
| 36.1-a1 |
36.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.99413$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.258814903$ |
$3.951338628$ |
3.769065024 |
\( -\frac{42875}{64} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -5 a\) , \( 20 a + 14\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-5a{x}+20a+14$ |
| 36.1-a2 |
36.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.99413$ |
$(3,a), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$9.776444709$ |
$3.951338628$ |
3.769065024 |
\( \frac{169125}{4} a + \frac{4141375}{4} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3$ |
| 36.1-a3 |
36.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.99413$ |
$(3,a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$1.086271634$ |
$3.951338628$ |
3.769065024 |
\( -\frac{169125}{4} a + 1077625 \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -16 a - 48\) , \( 68 a + 359\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3-{x}^2+\left(-16a-48\right){x}+68a+359$ |
| 36.3-a1 |
36.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.99413$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$3.258814903$ |
$3.951338628$ |
3.769065024 |
\( -\frac{42875}{64} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -20 a + 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(4a-5\right){x}-20a+34$ |
| 36.3-a2 |
36.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.99413$ |
$(3,a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$1.086271634$ |
$3.951338628$ |
3.769065024 |
\( \frac{169125}{4} a + \frac{4141375}{4} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 14 a - 63\) , \( -69 a + 427\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(14a-63\right){x}-69a+427$ |
| 36.3-a3 |
36.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
36.3 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.99413$ |
$(3,a+2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \) |
$9.776444709$ |
$3.951338628$ |
3.769065024 |
\( -\frac{169125}{4} a + 1077625 \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2-a{x}$ |
| 63.3-a1 |
63.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.3 |
\( 3^{2} \cdot 7 \) |
\( 3^{22} \cdot 7^{4} \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.272027391$ |
$2.785019355$ |
3.991563528 |
\( \frac{2364052463}{5250987} a - \frac{6727141172}{5250987} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -2 a - 73\) , \( -38 a - 122\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-73\right){x}-38a-122$ |
| 63.3-b1 |
63.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.3 |
\( 3^{2} \cdot 7 \) |
\( 3^{20} \cdot 7^{2} \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.819781294$ |
2.645198635 |
\( \frac{299119}{11907} a - \frac{2830123}{11907} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -7 a + 9\) , \( -a + 63\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-7a+9\right){x}-a+63$ |
| 63.3-b2 |
63.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.3 |
\( 3^{2} \cdot 7 \) |
\( 3^{28} \cdot 7 \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.409890647$ |
2.645198635 |
\( -\frac{1193890771}{413343} a + \frac{1255204366}{413343} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 3 a + 114\) , \( -61 a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(3a+114\right){x}-61a$ |
| 63.4-a1 |
63.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.4 |
\( 3^{2} \cdot 7 \) |
\( 3^{20} \cdot 7^{2} \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$4.819781294$ |
2.645198635 |
\( -\frac{299119}{11907} a - \frac{120524}{567} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3 a - 8\) , \( -a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-3a-8\right){x}-a+26$ |
| 63.4-a2 |
63.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.4 |
\( 3^{2} \cdot 7 \) |
\( 3^{28} \cdot 7 \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.409890647$ |
2.645198635 |
\( \frac{1193890771}{413343} a + \frac{2919695}{19683} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -13 a + 107\) , \( 164 a + 113\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-13a+107\right){x}+164a+113$ |
| 63.4-b1 |
63.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
63.4 |
\( 3^{2} \cdot 7 \) |
\( 3^{22} \cdot 7^{4} \) |
$2.29357$ |
$(3,a), (3,a+2), (7,a+6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.272027391$ |
$2.785019355$ |
3.991563528 |
\( -\frac{2364052463}{5250987} a - \frac{207766129}{250047} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -6 a - 57\) , \( -18 a - 78\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+a{x}^2+\left(-6a-57\right){x}-18a-78$ |
| 64.1-a1 |
64.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.30262$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$5.450043849$ |
4.785760240 |
\( 80 a + 1456 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 5\) , \( -3 a + 22\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(a+5\right){x}-3a+22$ |
| 64.1-b1 |
64.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{16} \cdot 3^{12} \) |
$2.30262$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$5.450043849$ |
4.785760240 |
\( -80 a + 1536 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 6\) , \( 3 a + 19\bigr] \) |
${y}^2={x}^3+a{x}^2+\left(-a+6\right){x}+3a+19$ |
| 83.1-a1 |
83.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
83.1 |
\( 83 \) |
\( 83^{2} \) |
$2.45724$ |
$(-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.177292294$ |
$6.604390094$ |
1.028190336 |
\( \frac{103823}{83} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+{x}$ |
| 87.1-a1 |
87.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
87.1 |
\( 3 \cdot 29 \) |
\( 3^{13} \cdot 29 \) |
$2.48632$ |
$(3,a), (29,a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.286673907$ |
2.038689778 |
\( -\frac{34723}{87} a + \frac{56110}{87} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -8 a + 3\) , \( 4 a + 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-8a+3\right){x}+4a+41$ |
| 87.4-a1 |
87.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
87.4 |
\( 3 \cdot 29 \) |
\( 3^{13} \cdot 29 \) |
$2.48632$ |
$(3,a+2), (29,a+15)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.286673907$ |
2.038689778 |
\( \frac{34723}{87} a + \frac{7129}{29} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2 a - 4\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-4\right){x}-a-2$ |
| 108.2-a1 |
108.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
108.2 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{24} \) |
$2.62442$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$1.359289146$ |
4.476041016 |
\( \frac{156590819}{27648} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -57 a - 126\) , \( -288 a + 405\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-57a-126\right){x}-288a+405$ |
| 108.2-a2 |
108.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
108.2 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{30} \) |
$2.62442$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.679644573$ |
4.476041016 |
\( \frac{555209567459}{23328} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -857 a - 2046\) , \( -25248 a + 10485\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-857a-2046\right){x}-25248a+10485$ |
| 108.3-a1 |
108.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
108.3 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{24} \) |
$2.62442$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$1.359289146$ |
4.476041016 |
\( \frac{156590819}{27648} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 57 a - 183\) , \( 288 a + 117\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(57a-183\right){x}+288a+117$ |
| 108.3-a2 |
108.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
108.3 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{30} \) |
$2.62442$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.679644573$ |
4.476041016 |
\( \frac{555209567459}{23328} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 857 a - 2903\) , \( 25248 a - 14763\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(857a-2903\right){x}+25248a-14763$ |
| 121.2-a1 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.70006$ |
$(11,a+3), (11,a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 1 \) |
$10.05214865$ |
$0.370308724$ |
1.634345201 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 121.2-a2 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.70006$ |
$(11,a+3), (11,a+7)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5^{2} \) |
$2.010429731$ |
$1.851543623$ |
1.634345201 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 121.2-a3 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.70006$ |
$(11,a+3), (11,a+7)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 1 \) |
$10.05214865$ |
$9.257718117$ |
1.634345201 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 144.1-a1 |
144.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.82012$ |
$(3,a), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 3 \) |
$1$ |
$3.776600821$ |
2.487214766 |
\( -131072 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a - 39\) , \( 36 a + 82\bigr] \) |
${y}^2={x}^3+a{x}^2+\left(-13a-39\right){x}+36a+82$ |
| 144.3-a1 |
144.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
144.3 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$2.82012$ |
$(3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 3 \) |
$1$ |
$3.776600821$ |
2.487214766 |
\( -131072 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 13 a - 52\) , \( -36 a + 118\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(13a-52\right){x}-36a+118$ |
| 147.1-a1 |
147.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{8} \) |
$2.83470$ |
$(3,a), (7,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$3.010021426$ |
1.321571097 |
\( -\frac{4096}{9} a + \frac{28672}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( -2\) , \( 6\bigr] \) |
${y}^2+a{y}={x}^3+\left(a+1\right){x}^2-2{x}+6$ |
| 147.3-a1 |
147.3-a |
$2$ |
$19$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.3 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{8} \) |
$2.83470$ |
$(3,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$19$ |
19B.4.1 |
$1$ |
\( 1 \) |
$3.177321592$ |
$3.425355151$ |
4.778457485 |
\( -\frac{419}{3} a + \frac{3401}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -4 a - 8\) , \( -4 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-4a-8\right){x}-4a+24$ |
| 147.3-a2 |
147.3-a |
$2$ |
$19$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.3 |
\( 3 \cdot 7^{2} \) |
\( 3^{19} \cdot 7^{8} \) |
$2.83470$ |
$(3,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$19$ |
19B.4.1 |
$1$ |
\( 1 \) |
$60.36911025$ |
$0.180281850$ |
4.778457485 |
\( -\frac{167810475310273823}{1162261467} a + \frac{2472632704310579117}{1162261467} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 311 a + 11437\) , \( -98529 a + 122853\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(311a+11437\right){x}-98529a+122853$ |
| 147.4-a1 |
147.4-a |
$2$ |
$19$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.4 |
\( 3 \cdot 7^{2} \) |
\( 3 \cdot 7^{8} \) |
$2.83470$ |
$(3,a+2), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$19$ |
19B.4.2 |
$1$ |
\( 1 \) |
$3.177321592$ |
$3.425355151$ |
4.778457485 |
\( \frac{419}{3} a + 994 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -5 a + 7\) , \( a + 28\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-5a+7\right){x}+a+28$ |
| 147.4-a2 |
147.4-a |
$2$ |
$19$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.4 |
\( 3 \cdot 7^{2} \) |
\( 3^{19} \cdot 7^{8} \) |
$2.83470$ |
$(3,a+2), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$19$ |
19B.4.2 |
$1$ |
\( 1 \) |
$60.36911025$ |
$0.180281850$ |
4.778457485 |
\( \frac{167810475310273823}{1162261467} a + \frac{768274076333435098}{387420489} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -320 a + 11767\) , \( 110286 a + 19187\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-320a+11767\right){x}+110286a+19187$ |
| 147.6-a1 |
147.6-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
147.6 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{8} \) |
$2.83470$ |
$(3,a+2), (7,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$3.010021426$ |
1.321571097 |
\( \frac{4096}{9} a + \frac{8192}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 3\) , \( -2 a + 9\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(2a-3\right){x}-2a+9$ |
| 161.1-a1 |
161.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
161.1 |
\( 7 \cdot 23 \) |
\( 7^{3} \cdot 23^{5} \) |
$2.89991$ |
$(7,a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.372068427$ |
$1.795729298$ |
4.400235209 |
\( -\frac{9185491898368}{2207665649} a - \frac{169699003219968}{2207665649} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -5 a - 26\) , \( -7 a - 46\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^3-a{x}^2+\left(-5a-26\right){x}-7a-46$ |
| 161.4-a1 |
161.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
161.4 |
\( 7 \cdot 23 \) |
\( 7^{3} \cdot 23^{5} \) |
$2.89991$ |
$(7,a+6), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$0.372068427$ |
$1.795729298$ |
4.400235209 |
\( \frac{9185491898368}{2207665649} a - \frac{25554927874048}{315380807} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 5 a - 31\) , \( 6 a - 52\bigr] \) |
${y}^2+a{y}={x}^3+\left(a-1\right){x}^2+\left(5a-31\right){x}+6a-52$ |
| 164.1-a1 |
164.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
164.1 |
\( 2^{2} \cdot 41 \) |
\( 2^{4} \cdot 3^{12} \cdot 41^{2} \) |
$2.91332$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$4$ |
\( 2^{2} \) |
$0.051697152$ |
$5.662340991$ |
2.056380937 |
\( -\frac{829502}{1681} a - \frac{7199103}{6724} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -a - 3\) , \( a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-a-3\right){x}+a+3$ |
| 164.2-a1 |
164.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
164.2 |
\( 2^{2} \cdot 41 \) |
\( 2^{4} \cdot 3^{12} \cdot 41^{2} \) |
$2.91332$ |
$(a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$4$ |
\( 2^{2} \) |
$0.051697152$ |
$5.662340991$ |
2.056380937 |
\( \frac{829502}{1681} a - \frac{10517111}{6724} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -3\) , \( -a + 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3-a{x}^2-3{x}-a+4$ |
| 189.2-a1 |
189.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
189.2 |
\( 3^{3} \cdot 7 \) |
\( 3^{23} \cdot 7 \) |
$3.01851$ |
$(3,a), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1.960681388$ |
$2.697280806$ |
2.321956789 |
\( -\frac{860943}{7} a + 885648 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 a - 164\) , \( 189 a - 593\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+\left(27a-164\right){x}+189a-593$ |
| 189.3-a1 |
189.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
189.3 |
\( 3^{3} \cdot 7 \) |
\( 3^{22} \cdot 7^{2} \) |
$3.01851$ |
$(3,a), (3,a+2), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.561394461$ |
$3.908412935$ |
3.853447990 |
\( -\frac{48269}{147} a + \frac{80660}{49} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2 a + 21\) , \( -2 a + 25\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-2a+21\right){x}-2a+25$ |
| 189.6-a1 |
189.6-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
189.6 |
\( 3^{3} \cdot 7 \) |
\( 3^{22} \cdot 7^{2} \) |
$3.01851$ |
$(3,a), (3,a+2), (7,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.561394461$ |
$3.908412935$ |
3.853447990 |
\( \frac{48269}{147} a + \frac{27673}{21} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3 a + 19\) , \( 4 a + 42\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(3a+19\right){x}+4a+42$ |
| 189.7-a1 |
189.7-a |
$1$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
189.7 |
\( 3^{3} \cdot 7 \) |
\( 3^{23} \cdot 7 \) |
$3.01851$ |
$(3,a+2), (7,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1.960681388$ |
$2.697280806$ |
2.321956789 |
\( \frac{860943}{7} a + \frac{5338593}{7} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 a - 137\) , \( -189 a - 404\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+\left(-27a-137\right){x}-189a-404$ |
| 196.1-a1 |
196.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$3.04608$ |
$(7,a), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2 \) |
$1.288829874$ |
$2.586758337$ |
5.855073996 |
\( -\frac{42875}{64} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -13 a + 26\) , \( 31 a - 155\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-13a+26\right){x}+31a-155$ |
| 196.1-a2 |
196.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{6} \) |
$3.04608$ |
$(7,a), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2 \) |
$1.288829874$ |
$2.586758337$ |
5.855073996 |
\( \frac{169125}{4} a + \frac{4141375}{4} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -35 a + 148\) , \( -99 a - 1410\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-35a+148\right){x}-99a-1410$ |
| 196.1-a3 |
196.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{6} \) |
$3.04608$ |
$(7,a), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2 \) |
$1.288829874$ |
$2.586758337$ |
5.855073996 |
\( -\frac{169125}{4} a + 1077625 \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( a + 26\) , \( 7 a - 66\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+{x}^2+\left(a+26\right){x}+7a-66$ |
| 196.2-a1 |
196.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$3.04608$ |
$(7,a), (7,a+6), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
0.864805626 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 196.2-a2 |
196.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$3.04608$ |
$(7,a), (7,a+6), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$9$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.864805626 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 196.2-a3 |
196.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$3.04608$ |
$(7,a), (7,a+6), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
0.864805626 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 196.2-a4 |
196.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$3.04608$ |
$(7,a), (7,a+6), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.313125702$ |
0.864805626 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 196.2-a5 |
196.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$3.04608$ |
$(7,a), (7,a+6), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.864805626 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
*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.
