| 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 |
| 2744.1-a1 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{4} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.072068378$ |
2.146800363 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( a + 3\) , \( -5 a - 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(a+3\right){x}-5a-5$ |
| 2744.1-a2 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{11} \cdot 7^{16} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.759008547$ |
2.146800363 |
\( -\frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 431 a - 132\) , \( 5054 a - 1007\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(431a-132\right){x}+5054a-1007$ |
| 2744.1-a3 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{14} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.036034189$ |
2.146800363 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -59 a - 132\) , \( 350 a + 365\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-59a-132\right){x}+350a+365$ |
| 2744.1-a4 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.072068378$ |
2.146800363 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -19 a - 42\) , \( -92 a - 115\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-19a-42\right){x}-92a-115$ |
| 2744.1-a5 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{11} \cdot 7^{16} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.518017094$ |
2.146800363 |
\( \frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1189 a - 1572\) , \( 24894 a + 34617\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1189a-1572\right){x}+24894a+34617$ |
| 2744.1-a6 |
2744.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.036034189$ |
2.146800363 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -299 a - 672\) , \( -5622 a - 6555\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-299a-672\right){x}-5622a-6555$ |
| 2744.1-b1 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.550645810$ |
1.557461546 |
\( -\frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 547 a - 183\) , \( 26317 a + 25687\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(547a-183\right){x}+26317a+25687$ |
| 2744.1-b2 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{15} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.202583242$ |
1.557461546 |
\( -\frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 183 a - 243\) , \( -1182 a + 1644\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(183a-243\right){x}-1182a+1644$ |
| 2744.1-b3 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{4} \cdot 7^{12} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.405166484$ |
1.557461546 |
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 43 a - 68\) , \( 225 a - 323\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(43a-68\right){x}+225a-323$ |
| 2744.1-b4 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{12} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.202583242$ |
1.557461546 |
\( -\frac{53744933616}{2401} a + \frac{76065896132}{2401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -433 a - 673\) , \( 6031 a + 8341\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-433a-673\right){x}+6031a+8341$ |
| 2744.1-b5 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.202583242$ |
1.557461546 |
\( \frac{110288896}{49} a + \frac{155981824}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 12\) , \( 104 a - 199\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-24a+12\right){x}+104a-199$ |
| 2744.1-b6 |
2744.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{15} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.101291621$ |
1.557461546 |
\( \frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 483 a - 1283\) , \( 15886 a - 16842\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(483a-1283\right){x}+15886a-16842$ |
| 2744.1-c1 |
2744.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{12} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.869996027$ |
1.983430308 |
\( \frac{97968}{343} a + \frac{138206}{343} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 9 a + 8\) , \( 80 a - 65\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(9a+8\right){x}+80a-65$ |
| 2744.1-c2 |
2744.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{11} \cdot 7^{15} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.869996027$ |
1.983430308 |
\( -\frac{3052852829}{117649} a + \frac{4720247008}{117649} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 139 a - 312\) , \( 1584 a - 1973\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(139a-312\right){x}+1584a-1973$ |
| 2744.1-d1 |
2744.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.171588031$ |
1.535544622 |
\( \frac{2746}{7} a + \frac{1254}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 9 a + 7\) , \( -14 a - 32\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a+7\right){x}-14a-32$ |
| 2744.1-e1 |
2744.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{3} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.276580075$ |
$7.282949672$ |
2.848676919 |
\( \frac{2746}{7} a + \frac{1254}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( a - 1\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}+a-1$ |
| 2744.1-f1 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{14} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.266922672$ |
$1.919579890$ |
2.898455552 |
\( -\frac{1326374192650}{5764801} a + \frac{1869046007278}{5764801} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -109 a - 243\) , \( 1684 a + 2062\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-109a-243\right){x}+1684a+2062$ |
| 2744.1-f2 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{7} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.133461336$ |
$7.678319560$ |
2.898455552 |
\( -\frac{43909218488}{7} a + \frac{62097019900}{7} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 61 a + 17\) , \( 66 a + 308\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(61a+17\right){x}+66a+308$ |
| 2744.1-f3 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{4} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.266922672$ |
$15.35663912$ |
2.898455552 |
\( -\frac{2274240}{49} a + \frac{3347024}{49} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9 a - 18\) , \( 3 a + 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-18\right){x}+3a+7$ |
| 2744.1-f4 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{7} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.533845344$ |
$7.678319560$ |
2.898455552 |
\( \frac{94208}{7} a + \frac{133120}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 7\) , \( -66 a + 92\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a-7\right){x}-66a+92$ |
| 2744.1-f5 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.133461336$ |
$7.678319560$ |
2.898455552 |
\( \frac{2777291400}{2401} a + \frac{3932074028}{2401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 81 a - 129\) , \( 141 a - 183\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(81a-129\right){x}+141a-183$ |
| 2744.1-f6 |
2744.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.266922672$ |
$3.839159780$ |
2.898455552 |
\( \frac{185561372918890}{49} a + \frac{262423410314434}{49} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -409 a + 361\) , \( 1317 a - 673\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-409a+361\right){x}+1317a-673$ |
| 2744.1-g1 |
2744.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{7} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.040235551$ |
1.442664393 |
\( -\frac{1029379622}{16807} a - \frac{1433160630}{16807} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -12 a + 8\) , \( 4 a - 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a+8\right){x}+4a-12$ |
| 2744.1-h1 |
2744.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{6} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.953100463$ |
1.397632072 |
\( \frac{97968}{343} a + \frac{138206}{343} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( a\) , \( 10 a - 15\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+a{x}+10a-15$ |
| 2744.1-h2 |
2744.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{11} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.953100463$ |
1.397632072 |
\( -\frac{3052852829}{117649} a + \frac{4720247008}{117649} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 51 a - 80\) , \( 242 a - 347\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(51a-80\right){x}+242a-347$ |
| 2744.1-i1 |
2744.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{8} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.834724458$ |
1.709333224 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -1\) , \( 11 a + 12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}-{x}+11a+12$ |
| 2744.1-i2 |
2744.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{11} \cdot 7^{11} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.208681114$ |
1.709333224 |
\( -\frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 90 a - 411\) , \( 1301 a - 2794\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(90a-411\right){x}+1301a-2794$ |
| 2744.1-i3 |
2744.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.834724458$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -40 a - 91\) , \( 231 a + 262\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-40a-91\right){x}+231a+262$ |
| 2744.1-i4 |
2744.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{11} \cdot 7^{11} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.834724458$ |
1.709333224 |
\( \frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 753 a - 1134\) , \( -5310 a + 7753\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(753a-1134\right){x}-5310a+7753$ |
| 2744.1-j1 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{15} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.003820431$ |
$0.981352412$ |
2.780985937 |
\( -\frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1552 a - 2446\) , \( 43596 a - 60166\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1552a-2446\right){x}+43596a-60166$ |
| 2744.1-j2 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.250477553$ |
$7.850819298$ |
2.780985937 |
\( -\frac{110288896}{49} a + \frac{155981824}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 64 a - 84\) , \( -282 a + 411\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(64a-84\right){x}-282a+411$ |
| 2744.1-j3 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{15} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.001910215$ |
$1.962704824$ |
2.780985937 |
\( \frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -68 a + 34\) , \( -296 a + 180\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-68a+34\right){x}-296a+180$ |
| 2744.1-j4 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{4} \cdot 7^{12} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.500955107$ |
$7.850819298$ |
2.780985937 |
\( \frac{4566144}{2401} a + \frac{14497232}{2401} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 12 a - 31\) , \( -28 a + 48\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-31\right){x}-28a+48$ |
| 2744.1-j5 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{12} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.001910215$ |
$3.925409649$ |
2.780985937 |
\( \frac{53744933616}{2401} a + \frac{76065896132}{2401} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 12 a - 276\) , \( 1148 a - 246\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-276\right){x}+1148a-246$ |
| 2744.1-j6 |
2744.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( - 2^{10} \cdot 7^{9} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.003820431$ |
$1.962704824$ |
2.780985937 |
\( \frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1528 a - 2026\) , \( 37884 a + 46738\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1528a-2026\right){x}+37884a+46738$ |
| 2744.1-k1 |
2744.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{13} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.048196170$ |
$2.959985084$ |
3.026274434 |
\( -\frac{1029379622}{16807} a - \frac{1433160630}{16807} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -83 a - 33\) , \( 274 a + 314\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-83a-33\right){x}+274a+314$ |
*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.
