| 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 |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \cdot 3^{12} \) |
$2.18519$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 1 \) |
$9.139015021$ |
$1.974258651$ |
4.173763512 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -47 a + 124\) , \( 189 a + 2053\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-47a+124\right){x}+189a+2053$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.18519$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 1 \) |
$1.827803004$ |
$9.871293256$ |
4.173763512 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -22 a + 49\) , \( 51 a + 199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-22a+49\right){x}+51a+199$ |
| 4.1-b1 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \cdot 3^{12} \) |
$2.18519$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 1 \) |
$9.139015021$ |
$1.974258651$ |
4.173763512 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 10 a + 153\) , \( -27 a + 161\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(10a+153\right){x}-27a+161$ |
| 4.1-b2 |
4.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.18519$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B |
$1$ |
\( 1 \) |
$1.827803004$ |
$9.871293256$ |
4.173763512 |
\( \frac{1331}{8} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -15 a + 103\) , \( 36 a + 44\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-15a+103\right){x}+36a+44$ |
| 27.2-a1 |
27.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{14} \cdot 7^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$9$ |
\( 2^{3} \) |
$1$ |
$3.179173933$ |
6.618829524 |
\( -\frac{2924207}{81} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -30 a - 333\) , \( -225 a - 135\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-30a-333\right){x}-225a-135$ |
| 27.2-a2 |
27.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{10} \cdot 7^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$36$ |
\( 2^{2} \) |
$1$ |
$1.589586966$ |
6.618829524 |
\( \frac{12214672127}{9} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -255 a - 6543\) , \( -12735 a - 150930\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-255a-6543\right){x}-12735a-150930$ |
| 27.2-b1 |
27.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{14} \cdot 5^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.179173933$ |
0.735425502 |
\( -\frac{2924207}{81} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -23 a + 73\) , \( -45 a + 695\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-23a+73\right){x}-45a+695$ |
| 27.2-b2 |
27.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{10} \cdot 5^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.589586966$ |
0.735425502 |
\( \frac{12214672127}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -383 a + 1558\) , \( -2115 a + 72515\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-383a+1558\right){x}-2115a+72515$ |
| 27.3-a1 |
27.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{14} \cdot 7^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$9$ |
\( 2^{3} \) |
$1$ |
$3.179173933$ |
6.618829524 |
\( -\frac{2924207}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -5 a - 401\) , \( -107 a - 1279\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-5a-401\right){x}-107a-1279$ |
| 27.3-a2 |
27.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \cdot 7^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$36$ |
\( 2^{2} \) |
$1$ |
$1.589586966$ |
6.618829524 |
\( \frac{12214672127}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 220 a - 6836\) , \( 6193 a - 181459\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(220a-6836\right){x}+6193a-181459$ |
| 27.3-b1 |
27.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{14} \cdot 5^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.179173933$ |
0.735425502 |
\( -\frac{2924207}{81} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 25 a + 50\) , \( 69 a + 700\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(25a+50\right){x}+69a+700$ |
| 27.3-b2 |
27.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \cdot 5^{12} \) |
$3.52221$ |
$(3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.589586966$ |
0.735425502 |
\( \frac{12214672127}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 385 a + 1175\) , \( 2499 a + 71575\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(385a+1175\right){x}+2499a+71575$ |
| 36.2-a1 |
36.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{14} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$36.77314910$ |
$0.694620345$ |
2.954423330 |
\( -\frac{4395631034341}{3145728} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -338 a + 1149\) , \( -543 a + 53577\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-338a+1149\right){x}-543a+53577$ |
| 36.2-a2 |
36.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{22} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$7.354629821$ |
$3.473101729$ |
2.954423330 |
\( \frac{5735339}{3888} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 7 a + 114\) , \( -33 a - 198\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(7a+114\right){x}-33a-198$ |
| 36.2-a3 |
36.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{32} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$3.677314910$ |
$1.736550864$ |
2.954423330 |
\( \frac{476379541}{236196} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -13 a + 174\) , \( 103 a - 930\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-13a+174\right){x}+103a-930$ |
| 36.2-a4 |
36.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$18.38657455$ |
$0.347310172$ |
2.954423330 |
\( \frac{18013780041269221}{9216} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -5458 a + 16509\) , \( -137759 a + 3865929\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-5458a+16509\right){x}-137759a+3865929$ |
| 36.2-b1 |
36.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{14} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
|
\( 2 \) |
$1$ |
$0.694620345$ |
2.954423330 |
\( -\frac{4395631034341}{3145728} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 338 a + 811\) , \( 543 a + 53034\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(338a+811\right){x}+543a+53034$ |
| 36.2-b2 |
36.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{22} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
|
\( 2 \) |
$1$ |
$3.473101729$ |
2.954423330 |
\( \frac{5735339}{3888} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -7 a + 121\) , \( 33 a - 231\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(-7a+121\right){x}+33a-231$ |
| 36.2-b3 |
36.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{32} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
|
\( 2^{3} \) |
$1$ |
$1.736550864$ |
2.954423330 |
\( \frac{476379541}{236196} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 13 a + 161\) , \( -103 a - 827\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(13a+161\right){x}-103a-827$ |
| 36.2-b4 |
36.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
36.2 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$3.78486$ |
$(3,a), (3,a+2), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
|
\( 2^{3} \) |
$1$ |
$0.347310172$ |
2.954423330 |
\( \frac{18013780041269221}{9216} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 5458 a + 11051\) , \( 137759 a + 3728170\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+\left(5458a+11051\right){x}+137759a+3728170$ |
| 44.1-a1 |
44.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{2} \cdot 7^{12} \cdot 11^{4} \) |
$3.97958$ |
$(11,a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.757034834$ |
$5.289539352$ |
4.299843184 |
\( \frac{9888969}{29282} a + \frac{25798837}{14641} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -4 a + 94\) , \( 36 a + 112\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+{x}^2+\left(-4a+94\right){x}+36a+112$ |
| 44.1-b1 |
44.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{2} \cdot 5^{12} \cdot 11^{4} \) |
$3.97958$ |
$(11,a+1), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.376995600$ |
$5.289539352$ |
3.690358166 |
\( \frac{9888969}{29282} a + \frac{25798837}{14641} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a + 96\) , \( -15 a - 356\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-3a+96\right){x}-15a-356$ |
| 44.2-a1 |
44.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{2} \cdot 7^{12} \cdot 11^{4} \) |
$3.97958$ |
$(11,a+9), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.757034834$ |
$5.289539352$ |
4.299843184 |
\( -\frac{9888969}{29282} a + \frac{61486643}{29282} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 3 a + 90\) , \( -37 a + 148\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(3a+90\right){x}-37a+148$ |
| 44.2-b1 |
44.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{2} \cdot 5^{12} \cdot 11^{4} \) |
$3.97958$ |
$(11,a+9), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.376995600$ |
$5.289539352$ |
3.690358166 |
\( -\frac{9888969}{29282} a + \frac{61486643}{29282} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a + 167\) , \( 11 a - 463\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(4a+167\right){x}+11a-463$ |
| 52.1-a1 |
52.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{26} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$8.351691627$ |
$0.560128502$ |
4.328590596 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -35944\) , \( -2868878\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-35944{x}-2868878$ |
| 52.1-a2 |
52.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.170442686$ |
$3.920899519$ |
4.328590596 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -454\) , \( 5812\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-454{x}+5812$ |
| 52.1-b1 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$4.14930$ |
$(13,a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$0.560128502$ |
0.518289083 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 52.1-b2 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.14930$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.518289083 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-c1 |
52.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{14} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$3.363778387$ |
$0.896934130$ |
12.56275321 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -77659\) , \( -8336303\bigr] \) |
${y}^2+{x}{y}={x}^3-77659{x}-8336303$ |
| 52.1-c2 |
52.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{6} \cdot 13^{18} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.121259462$ |
$2.690802392$ |
12.56275321 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -764\) , \( -16264\bigr] \) |
${y}^2+{x}{y}={x}^3-764{x}-16264$ |
| 52.1-c3 |
52.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$3.363778387$ |
$8.072407178$ |
12.56275321 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 81\) , \( 467\bigr] \) |
${y}^2+{x}{y}={x}^3+81{x}+467$ |
| 52.1-d1 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.627730073$ |
$0.896934130$ |
6.079107737 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 52.1-d2 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$4.883190221$ |
$2.690802392$ |
6.079107737 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 52.1-d3 |
52.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$4.14930$ |
$(13,a+6), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$14.64957066$ |
$8.072407178$ |
6.079107737 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 92.1-c1 |
92.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{20} \cdot 23^{2} \) |
$4.78543$ |
$(23,a+11), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$3.167384488$ |
$2.403591625$ |
8.805537464 |
\( -\frac{116930169}{23552} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-10{x}-12$ |
| 92.1-c2 |
92.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{10} \cdot 23^{4} \) |
$4.78543$ |
$(23,a+11), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$6.334768976$ |
$1.201795812$ |
8.805537464 |
\( \frac{545138290809}{16928} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-170{x}-812$ |
| 92.1-d1 |
92.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{20} \cdot 13^{12} \cdot 23^{2} \) |
$4.78543$ |
$(23,a+11), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.411224795$ |
$2.403591625$ |
3.923297867 |
\( -\frac{116930169}{23552} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1722\) , \( -31495\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1722{x}-31495$ |
| 92.1-d2 |
92.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( 2^{10} \cdot 13^{12} \cdot 23^{4} \) |
$4.78543$ |
$(23,a+11), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$2.822449591$ |
$1.201795812$ |
3.923297867 |
\( \frac{545138290809}{16928} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -28762\) , \( -1870215\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-28762{x}-1870215$ |
| 100.2-a1 |
100.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{6} \) |
$4.88623$ |
$(5,a), (5,a+4), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$2.409350082$ |
$3.052416071$ |
5.103748809 |
\( \frac{16194277}{8000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -27 a + 66\) , \( 95 a + 290\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-27a+66\right){x}+95a+290$ |
| 100.2-a2 |
100.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{12} \) |
$4.88623$ |
$(5,a), (5,a+4), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.409350082$ |
$1.526208035$ |
5.103748809 |
\( \frac{10260751717}{125000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -67 a + 186\) , \( 271 a + 4298\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-67a+186\right){x}+271a+4298$ |
| 100.2-b1 |
100.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{6} \) |
$4.88623$ |
$(5,a), (5,a+4), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$2.409350082$ |
$3.052416071$ |
5.103748809 |
\( \frac{16194277}{8000} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -10 a + 114\) , \( 8 a - 234\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-10a+114\right){x}+8a-234$ |
| 100.2-b2 |
100.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{12} \) |
$4.88623$ |
$(5,a), (5,a+4), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.409350082$ |
$1.526208035$ |
5.103748809 |
\( \frac{10260751717}{125000} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 30 a + 194\) , \( -48 a + 950\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(30a+194\right){x}-48a+950$ |
*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.
