| 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 |
| 77.1-a1 |
77.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7 \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$6.801526433$ |
$42.50483853$ |
3.660638887 |
\( -\frac{3620807}{77} a - \frac{13473085}{77} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 7 a + 15\) , \( 4 a + 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+15\right){x}+4a+52$ |
| 77.1-a2 |
77.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7^{3} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$2.267175477$ |
$4.722759837$ |
3.660638887 |
\( -\frac{4739950783}{65219} a + \frac{23189184708}{65219} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 42 a - 155\) , \( 228 a - 1038\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(42a-155\right){x}+228a-1038$ |
| 77.1-a3 |
77.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{3} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$4.534350955$ |
$2.361379918$ |
3.660638887 |
\( -\frac{1921257763497199}{41503} a + \frac{9390113368382893}{41503} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 592 a - 2850\) , \( 15694 a - 76652\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(592a-2850\right){x}+15694a-76652$ |
| 77.1-a4 |
77.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{2} \cdot 11 \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$13.60305286$ |
$21.25241926$ |
3.660638887 |
\( \frac{1443189816791}{77} a + \frac{5610375344526}{77} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 12 a - 15\) , \( 20 a - 44\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-15\right){x}+20a-44$ |
| 77.1-b1 |
77.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.192052107$ |
$10.23860076$ |
3.585372697 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+2{x}$ |
| 77.1-c1 |
77.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7 \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( \frac{3620807}{77} a - \frac{17093892}{77} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5 a - 8\) , \( 10 a - 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5a-8\right){x}+10a-33$ |
| 77.1-c2 |
77.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{2} \cdot 11 \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( -\frac{1443189816791}{77} a + \frac{7053565161317}{77} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 55 a - 253\) , \( 466 a - 2263\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(55a-253\right){x}+466a-2263$ |
| 77.1-c3 |
77.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7^{3} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( \frac{4739950783}{65219} a + \frac{18449233925}{65219} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -5 a + 37\) , \( 34 a - 157\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a+37\right){x}+34a-157$ |
| 77.1-c4 |
77.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{3} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( \frac{1921257763497199}{41503} a + \frac{7468855604885694}{41503} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 50 a - 293\) , \( 430 a - 2049\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(50a-293\right){x}+430a-2049$ |
| 77.1-d1 |
77.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{4} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.438142950$ |
$3.210187340$ |
3.846910527 |
\( \frac{4657463}{41503} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 36 a + 137\) , \( -619 a - 2411\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(36a+137\right){x}-619a-2411$ |
| 77.1-d2 |
77.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{12} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.438142950$ |
$3.210187340$ |
3.846910527 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 469 a - 2246\) , \( 10656 a - 52022\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(469a-2246\right){x}+10656a-52022$ |
| 77.1-e1 |
77.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.380901696$ |
$21.59210152$ |
1.666249113 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$ |
| 77.1-e2 |
77.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{12} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.142705089$ |
$2.399122391$ |
1.666249113 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$ |
| 77.1-e3 |
77.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$3.428115269$ |
$0.266569154$ |
1.666249113 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 77.1-f1 |
77.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7 \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$6.801526433$ |
$42.50483853$ |
3.660638887 |
\( \frac{3620807}{77} a - \frac{17093892}{77} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 4\) , \( 2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+4\right){x}+2a+4$ |
| 77.1-f2 |
77.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{2} \cdot 11 \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$13.60305286$ |
$21.25241926$ |
3.660638887 |
\( -\frac{1443189816791}{77} a + \frac{7053565161317}{77} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -44 a - 171\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-21\right){x}-44a-171$ |
| 77.1-f3 |
77.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7^{3} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$2.267175477$ |
$4.722759837$ |
3.660638887 |
\( \frac{4739950783}{65219} a + \frac{18449233925}{65219} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 131\) , \( -392 a - 1527\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-32a-131\right){x}-392a-1527$ |
| 77.1-f4 |
77.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{3} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$4.534350955$ |
$2.361379918$ |
3.660638887 |
\( \frac{1921257763497199}{41503} a + \frac{7468855604885694}{41503} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -582 a - 2276\) , \( -18553 a - 72125\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-582a-2276\right){x}-18553a-72125$ |
| 77.1-g1 |
77.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7 \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( -\frac{3620807}{77} a - \frac{13473085}{77} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -6 a - 2\) , \( -10 a - 23\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6a-2\right){x}-10a-23$ |
| 77.1-g2 |
77.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( - 7^{3} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( -\frac{4739950783}{65219} a + \frac{23189184708}{65219} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 4 a + 33\) , \( -34 a - 123\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a+33\right){x}-34a-123$ |
| 77.1-g3 |
77.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{3} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( -\frac{1921257763497199}{41503} a + \frac{9390113368382893}{41503} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -51 a - 242\) , \( -430 a - 1619\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-51a-242\right){x}-430a-1619$ |
| 77.1-g4 |
77.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{2} \cdot 11 \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$7.332154545$ |
1.671153117 |
\( \frac{1443189816791}{77} a + \frac{5610375344526}{77} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -56 a - 197\) , \( -466 a - 1797\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-56a-197\right){x}-466a-1797$ |
| 77.1-h1 |
77.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.175784754$ |
$9.086092621$ |
2.912279051 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 18 a + 70\) , \( -20 a - 78\bigr] \) |
${y}^2+{y}={x}^{3}+\left(18a+70\right){x}-20a-78$ |
| 77.1-i1 |
77.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{6} \cdot 11^{4} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.847304922$ |
$7.031061357$ |
2.715659066 |
\( \frac{4657463}{41503} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}+11$ |
| 77.1-i2 |
77.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{12} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.694609845$ |
$7.031061357$ |
2.715659066 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-51{x}+110$ |
| 77.1-j1 |
77.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{2} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.602881548$ |
1.099275660 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -803 a - 3120\) , \( -24422 a - 94941\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-803a-3120\right){x}-24422a-94941$ |
| 77.1-j2 |
77.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{12} \cdot 11^{6} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$0.602881548$ |
1.099275660 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -443 a - 1720\) , \( -48462 a - 188396\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-443a-1720\right){x}-48462a-188396$ |
| 77.1-j3 |
77.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
77.1 |
\( 7 \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.32277$ |
$(a+3), (a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.602881548$ |
1.099275660 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 3967 a + 15430\) , \( 1269148 a + 4933819\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3967a+15430\right){x}+1269148a+4933819$ |
*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.
