| 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 |
| 228.1-a1 |
228.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.498365743$ |
6.487178073 |
\( \frac{50586025225}{2432} a - \frac{648752782793}{7296} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4065 a - 17370\) , \( 271290 a - 1159743\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4065a-17370\right){x}+271290a-1159743$ |
| 228.1-b1 |
228.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{21} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.785056116$ |
1.891491668 |
\( -\frac{1627749557}{4202496} a - \frac{2731557865}{2101248} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -8464 a - 27714\) , \( -1046589 a - 3427495\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8464a-27714\right){x}-1046589a-3427495$ |
| 228.1-c1 |
228.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$8.115846388$ |
4.299880458 |
\( -\frac{197323441}{2736} a - \frac{771501277}{2736} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 2 a - 7\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(2a-7\right){x}-2a+3$ |
| 228.1-d1 |
228.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{20} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$3.533391254$ |
9.360182093 |
\( -\frac{69173457625}{42633378} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1033091 a - 3383285\) , \( 1593926133 a + 5219976135\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1033091a-3383285\right){x}+1593926133a+5219976135$ |
| 228.1-d2 |
228.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$14.13356501$ |
9.360182093 |
\( -\frac{29605499548772875}{8208} a + \frac{63280529891672125}{4104} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -455 a - 1493\) , \( 6825 a + 22353\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-455a-1493\right){x}+6825a+22353$ |
| 228.1-d3 |
228.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{4} \cdot 3^{10} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$14.13356501$ |
9.360182093 |
\( \frac{96386901625}{18468} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1153891 a - 3778895\) , \( 1308542283 a + 4285367651\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1153891a-3778895\right){x}+1308542283a+4285367651$ |
| 228.1-d4 |
228.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$14.13356501$ |
9.360182093 |
\( \frac{29605499548772875}{8208} a + \frac{96955560234571375}{8208} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 455 a - 1948\) , \( -6825 a + 29178\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(455a-1948\right){x}-6825a+29178$ |
| 228.1-e1 |
228.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{21} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.785056116$ |
1.891491668 |
\( \frac{1627749557}{4202496} a - \frac{7090865287}{4202496} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 8464 a - 36178\) , \( 1046589 a - 4474084\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(8464a-36178\right){x}+1046589a-4474084$ |
| 228.1-f1 |
228.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{36} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.276517915$ |
0.659262467 |
\( -\frac{146610587591375}{119537664} a - \frac{553912379914747}{119537664} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2637 a - 8642\) , \( -148236 a - 485468\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2637a-8642\right){x}-148236a-485468$ |
| 228.1-f2 |
228.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.488661241$ |
0.659262467 |
\( -\frac{12749851}{415872} a + \frac{163604263}{1247616} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3 a + 13\) , \( -585 a - 1919\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+13\right){x}-585a-1919$ |
| 228.1-g1 |
228.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{36} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
$0.060152355$ |
$6.016849312$ |
6.711388494 |
\( \frac{146610587591375}{119537664} a - \frac{116753827917687}{19922944} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -109294 a - 357929\) , \( 38220950 a + 125170447\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-109294a-357929\right){x}+38220950a+125170447$ |
| 228.1-g2 |
228.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \) |
$0.020050785$ |
$6.016849312$ |
6.711388494 |
\( \frac{12749851}{415872} a + \frac{62677355}{623808} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 2066 a + 6766\) , \( 253346 a + 829687\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2066a+6766\right){x}+253346a+829687$ |
| 228.1-h1 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{12} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.275427410$ |
3.939975182 |
\( -\frac{8078253774625}{846825858} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \) |
${y}^2+{x}{y}={x}^{3}-418{x}-3610$ |
| 228.1-h2 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$2.478846691$ |
3.939975182 |
\( \frac{3616805375}{2105352} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+32{x}+8$ |
| 228.1-h3 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$9.915386767$ |
3.939975182 |
\( \frac{57066625}{32832} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-8{x}$ |
| 228.1-h4 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3 \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.101709640$ |
3.939975182 |
\( -\frac{25477549476528524375}{17328} a + \frac{108914414920560011125}{17328} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -10156 a - 33260\) , \( -1012867 a - 3317057\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10156a-33260\right){x}-1012867a-3317057$ |
| 228.1-h5 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{15} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$9.915386767$ |
3.939975182 |
\( -\frac{13676826625}{700416} a + \frac{107616800875}{350208} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2127 a - 9087\) , \( -101691 a + 434709\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2127a-9087\right){x}-101691a+434709$ |
| 228.1-h6 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{15} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$9.915386767$ |
3.939975182 |
\( \frac{13676826625}{700416} a + \frac{201556775125}{700416} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2126 a - 6960\) , \( 99563 a + 326059\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2126a-6960\right){x}+99563a+326059$ |
| 228.1-h7 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{4} \cdot 3^{2} \cdot 19^{6} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.101709640$ |
3.939975182 |
\( \frac{8671983378625}{82308} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -428\) , \( -3444\bigr] \) |
${y}^2+{x}{y}={x}^{3}-428{x}-3444$ |
| 228.1-h8 |
228.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3 \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.101709640$ |
3.939975182 |
\( \frac{25477549476528524375}{17328} a + \frac{41718432722015743375}{8664} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 10157 a - 43417\) , \( 1002709 a - 4286507\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10157a-43417\right){x}+1002709a-4286507$ |
| 228.1-i1 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{24} \cdot 19^{8} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.326467847$ |
$0.633866730$ |
2.672812530 |
\( -\frac{16576888679672833}{2216253521952} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -64169211 a - 210148851\) , \( 603052792193 a + 1974947972293\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-64169211a-210148851\right){x}+603052792193a+1974947972293$ |
| 228.1-i2 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( - 2^{50} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.652935694$ |
$1.267733460$ |
2.672812530 |
\( -\frac{173545548222105857}{188016488349696} a + \frac{388781211214657643}{94008244174848} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2059 a + 6740\) , \( 281466 a + 921776\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(2059a+6740\right){x}+281466a+921776$ |
| 228.1-i3 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( - 2^{50} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.652935694$ |
$1.267733460$ |
2.672812530 |
\( \frac{173545548222105857}{188016488349696} a + \frac{604016874207209429}{188016488349696} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2059 a + 8799\) , \( -281466 a + 1203242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-2059a+8799\right){x}-281466a+1203242$ |
| 228.1-i4 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{40} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.326467847$ |
$2.535466920$ |
2.672812530 |
\( \frac{4824238966273}{537919488} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -4252411 a - 13926291\) , \( 8325010913 a + 27263721573\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4252411a-13926291\right){x}+8325010913a+27263721573$ |
| 228.1-i5 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3^{12} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.663233923$ |
$2.535466920$ |
2.672812530 |
\( \frac{18120364883707393}{269485056} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -66102011 a - 216478611\) , \( 568251032033 a + 1860975088741\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-66102011a-216478611\right){x}+568251032033a+1860975088741$ |
| 228.1-i6 |
228.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.326467847$ |
$2.535466920$ |
2.672812530 |
\( \frac{74220219816682217473}{16416} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -1057628411 a - 3463645491\) , \( 36374182046273 a + 119122435060741\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1057628411a-3463645491\right){x}+36374182046273a+119122435060741$ |
| 228.1-j1 |
228.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.170606725$ |
$10.03516982$ |
2.721226509 |
\( -\frac{197323441}{2736} a - \frac{771501277}{2736} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -20689 a - 67751\) , \( 3186545 a + 10435669\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20689a-67751\right){x}+3186545a+10435669$ |
| 228.1-k1 |
228.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.238115403$ |
$13.76401557$ |
1.736421720 |
\( -\frac{50586025225}{2432} a - \frac{248497353559}{3648} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -13 a + 58\) , \( 237 a - 1022\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-13a+58\right){x}+237a-1022$ |
| 228.1-l1 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{24} \cdot 19^{8} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$0.077031086$ |
4.081206648 |
\( -\frac{16576888679672833}{2216253521952} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5312\) , \( -167551\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5312{x}-167551$ |
| 228.1-l2 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( - 2^{50} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$1.232497379$ |
4.081206648 |
\( -\frac{173545548222105857}{188016488349696} a + \frac{388781211214657643}{94008244174848} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 31110 a - 132991\) , \( -5096364 a + 21786529\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(31110a-132991\right){x}-5096364a+21786529$ |
| 228.1-l3 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( - 2^{50} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$1.232497379$ |
4.081206648 |
\( \frac{173545548222105857}{188016488349696} a + \frac{604016874207209429}{188016488349696} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -31111 a - 101880\) , \( 5096363 a + 16690166\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-31111a-101880\right){x}+5096363a+16690166$ |
| 228.1-l4 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{40} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 5^{2} \) |
$1$ |
$1.232497379$ |
4.081206648 |
\( \frac{4824238966273}{537919488} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2431\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2431$ |
| 228.1-l5 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{20} \cdot 3^{12} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.308124344$ |
4.081206648 |
\( \frac{18120364883707393}{269485056} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5472\) , \( -158079\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5472{x}-158079$ |
| 228.1-l6 |
228.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$0.077031086$ |
4.081206648 |
\( \frac{74220219816682217473}{16416} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -87552\) , \( -10007679\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-87552{x}-10007679$ |
| 228.1-m1 |
228.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.238115403$ |
$13.76401557$ |
1.736421720 |
\( \frac{50586025225}{2432} a - \frac{648752782793}{7296} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 12 a + 46\) , \( -238 a - 784\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+46\right){x}-238a-784$ |
| 228.1-n1 |
228.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$8.115846388$ |
4.299880458 |
\( \frac{197323441}{2736} a - \frac{484412359}{1368} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 5\) , \( a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-5\right){x}+a+1$ |
| 228.1-o1 |
228.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{20} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.213056302$ |
$0.583042285$ |
2.537040597 |
\( -\frac{69173457625}{42633378} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -85\) , \( -473\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-85{x}-473$ |
| 228.1-o2 |
228.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.213056302$ |
$2.332169141$ |
2.537040597 |
\( -\frac{29605499548772875}{8208} a + \frac{63280529891672125}{4104} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 35436 a - 151484\) , \( 7007444 a - 29956246\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(35436a-151484\right){x}+7007444a-29956246$ |
| 228.1-o3 |
228.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{4} \cdot 3^{10} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.106528151$ |
$2.332169141$ |
2.537040597 |
\( \frac{96386901625}{18468} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -95\) , \( -399\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-95{x}-399$ |
| 228.1-o4 |
228.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.213056302$ |
$2.332169141$ |
2.537040597 |
\( \frac{29605499548772875}{8208} a + \frac{96955560234571375}{8208} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -35437 a - 116048\) , \( -7007445 a - 22948802\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-35437a-116048\right){x}-7007445a-22948802$ |
| 228.1-p1 |
228.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{36} \cdot 3^{2} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
$0.060152355$ |
$6.016849312$ |
6.711388494 |
\( -\frac{146610587591375}{119537664} a - \frac{553912379914747}{119537664} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 109294 a - 467223\) , \( -38220950 a + 163391397\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(109294a-467223\right){x}-38220950a+163391397$ |
| 228.1-p2 |
228.1-p |
$2$ |
$3$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \) |
$0.020050785$ |
$6.016849312$ |
6.711388494 |
\( -\frac{12749851}{415872} a + \frac{163604263}{1247616} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2066 a + 8832\) , \( -253346 a + 1083033\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2066a+8832\right){x}-253346a+1083033$ |
| 228.1-q1 |
228.1-q |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.170606725$ |
$10.03516982$ |
2.721226509 |
\( \frac{197323441}{2736} a - \frac{484412359}{1368} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 20690 a - 88440\) , \( -3165856 a + 13533774\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20690a-88440\right){x}-3165856a+13533774$ |
| 228.1-r1 |
228.1-r |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{21} \cdot 3^{5} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 13 \) |
$0.018035926$ |
$8.937065138$ |
5.550975306 |
\( -\frac{1627749557}{4202496} a - \frac{2731557865}{2101248} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 9 a - 29\) , \( -181 a + 779\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-29\right){x}-181a+779$ |
| 228.1-s1 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{12} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.129702711$ |
$2.380767667$ |
0.895441686 |
\( -\frac{8078253774625}{846825858} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5049692 a - 16537318\) , \( 13049407660 a + 42735729826\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5049692a-16537318\right){x}+13049407660a+42735729826$ |
| 228.1-s2 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{4} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.709900903$ |
$2.380767667$ |
0.895441686 |
\( \frac{3616805375}{2105352} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 386308 a + 1265132\) , \( -19979150 a - 65430062\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(386308a+1265132\right){x}-19979150a-65430062$ |
| 228.1-s3 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.354950451$ |
$9.523070670$ |
0.895441686 |
\( \frac{57066625}{32832} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -96892 a - 317308\) , \( -2306310 a - 7552974\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-96892a-317308\right){x}-2306310a-7552974$ |
| 228.1-s4 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{5} \cdot 3 \cdot 19^{3} \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.129702711$ |
$9.523070670$ |
0.895441686 |
\( -\frac{25477549476528524375}{17328} a + \frac{108914414920560011125}{17328} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 29535 a - 126260\) , \( -5355845 a + 22895794\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(29535a-126260\right){x}-5355845a+22895794$ |
| 228.1-s5 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{15} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.709900903$ |
$9.523070670$ |
0.895441686 |
\( -\frac{13676826625}{700416} a + \frac{107616800875}{350208} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -365 a - 1195\) , \( 7195 a + 23563\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-365a-1195\right){x}+7195a+23563$ |
| 228.1-s6 |
228.1-s |
$8$ |
$12$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
228.1 |
\( 2^{2} \cdot 3 \cdot 19 \) |
\( 2^{15} \cdot 3^{3} \cdot 19 \) |
$2.62156$ |
$(a-4), (a+3), (4a+13), (10a-43)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.709900903$ |
$9.523070670$ |
0.895441686 |
\( \frac{13676826625}{700416} a + \frac{201556775125}{700416} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 365 a - 1560\) , \( -7195 a + 30758\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(365a-1560\right){x}-7195a+30758$ |
*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.
