| 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 |
| 784.1-a1 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{2} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -682\) , \( 6990\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-682{x}+6990$ |
| 784.1-a2 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}-2$ |
| 784.1-a3 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( 46\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}+46$ |
| 784.1-a4 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( -\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 220 a - 362\) , \( 2320 a - 3330\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(220a-362\right){x}+2320a-3330$ |
| 784.1-a5 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -142\) , \( 558\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-142{x}+558$ |
| 784.1-a6 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{15} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( -\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 520 a - 1422\) , \( -16000 a + 16302\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(520a-1422\right){x}-16000a+16302$ |
| 784.1-a7 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( -\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 57920 a - 92842\) , \( -9795840 a + 14293838\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(57920a-92842\right){x}-9795840a+14293838$ |
| 784.1-a8 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -42\) , \( -98\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-42{x}-98$ |
| 784.1-a9 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{15} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -520 a - 1422\) , \( 16000 a + 16302\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-520a-1422\right){x}+16000a+16302$ |
| 784.1-a10 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.513854052$ |
1.242335014 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -10922\) , \( 441166\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-10922{x}+441166$ |
| 784.1-a11 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -220 a - 362\) , \( -2320 a - 3330\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-220a-362\right){x}-2320a-3330$ |
| 784.1-a12 |
784.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.756927026$ |
1.242335014 |
\( \frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -57920 a - 92842\) , \( 9795840 a + 14293838\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-57920a-92842\right){x}+9795840a+14293838$ |
| 784.1-b1 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( -\frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 115 a - 122\) , \( -322 a + 1587\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(115a-122\right){x}-322a+1587$ |
| 784.1-b2 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.165276793$ |
1.472647733 |
\( -\frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 15 a + 18\) , \( -30 a - 43\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+18\right){x}-30a-43$ |
| 784.1-b3 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{6} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$16.66110717$ |
1.472647733 |
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a - 7\) , \( -7 a - 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-7\right){x}-7a-9$ |
| 784.1-b4 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$16.66110717$ |
1.472647733 |
\( -\frac{53744933616}{2401} a + \frac{76065896132}{2401} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a - 52\) , \( 84 a + 159\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-52\right){x}+84a+159$ |
| 784.1-b5 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( \frac{110288896}{49} a + \frac{155981824}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 7\) , \( -23 a + 32\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+7\right){x}-23a+32$ |
| 784.1-b6 |
784.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( \frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 194 a - 314\) , \( -2200 a + 3186\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(194a-314\right){x}-2200a+3186$ |
| 784.1-c1 |
784.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.239919898$ |
$22.75712104$ |
1.930361270 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}$ |
| 784.1-c2 |
784.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.239919898$ |
$11.37856052$ |
1.930361270 |
\( -\frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 50 a - 91\) , \( -274 a + 370\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(50a-91\right){x}-274a+370$ |
| 784.1-c3 |
784.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.119959949$ |
$22.75712104$ |
1.930361270 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -11\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-11{x}+10$ |
| 784.1-c4 |
784.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{5} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.239919898$ |
$11.37856052$ |
1.930361270 |
\( \frac{4347206325605}{2401} a + \frac{6147883179496}{2401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -50 a - 91\) , \( 274 a + 370\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-50a-91\right){x}+274a+370$ |
| 784.1-d1 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.069108576$ |
$10.54517411$ |
1.992969164 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}$ |
| 784.1-d2 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{11} \cdot 7^{10} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.133638572$ |
$5.272587057$ |
1.992969164 |
\( -\frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 90 a - 94\) , \( -368 a + 642\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(90a-94\right){x}-368a+642$ |
| 784.1-d3 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{8} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.267277144$ |
$10.54517411$ |
1.992969164 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -14\) , \( 10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-14{x}+10$ |
| 784.1-d4 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.534554288$ |
$10.54517411$ |
1.992969164 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}-6$ |
| 784.1-d5 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{11} \cdot 7^{10} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.133638572$ |
$5.272587057$ |
1.992969164 |
\( \frac{29774895462729}{5764801} a + \frac{42111203990760}{5764801} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -90 a - 94\) , \( 368 a + 642\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-90a-94\right){x}+368a+642$ |
| 784.1-d6 |
784.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.069108576$ |
$2.636293528$ |
1.992969164 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -74\) , \( -286\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-74{x}-286$ |
| 784.1-e1 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( -\frac{1159856388322676}{5764801} a + \frac{1640242904389426}{5764801} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -194 a - 314\) , \( 2200 a + 3186\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-194a-314\right){x}+2200a+3186$ |
| 784.1-e2 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( -\frac{110288896}{49} a + \frac{155981824}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a + 7\) , \( 23 a + 32\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+7\right){x}+23a+32$ |
| 784.1-e3 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.165276793$ |
1.472647733 |
\( \frac{13282665232}{5764801} a + \frac{23566456972}{5764801} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a + 18\) , \( 30 a - 43\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+18\right){x}+30a-43$ |
| 784.1-e4 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{6} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$16.66110717$ |
1.472647733 |
\( \frac{4566144}{2401} a + \frac{14497232}{2401} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a - 7\) , \( 7 a - 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-7\right){x}+7a-9$ |
| 784.1-e5 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$16.66110717$ |
1.472647733 |
\( \frac{53744933616}{2401} a + \frac{76065896132}{2401} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 25 a - 52\) , \( -84 a + 159\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-52\right){x}-84a+159$ |
| 784.1-e6 |
784.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{10} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.330553587$ |
1.472647733 |
\( \frac{69495892205440052}{49} a + \frac{98282033286152638}{49} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -115 a - 122\) , \( 322 a + 1587\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-115a-122\right){x}+322a+1587$ |
| 784.1-f1 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( -\frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1562 a - 3681\) , \( -52607 a + 96844\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1562a-3681\right){x}-52607a+96844$ |
| 784.1-f2 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( -\frac{13219923200}{117649} a + \frac{18683377472}{117649} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 41\) , \( -51 a + 132\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(22a-41\right){x}-51a+132$ |
| 784.1-f3 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( -\frac{210688}{49} a + \frac{302912}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 1\) , \( a - 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a-1\right){x}+a-4$ |
| 784.1-f4 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( \frac{210688}{49} a + \frac{302912}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 1\) , \( -a - 4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-1\right){x}-a-4$ |
| 784.1-f5 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( \frac{13219923200}{117649} a + \frac{18683377472}{117649} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 41\) , \( 51 a + 132\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-22a-41\right){x}+51a+132$ |
| 784.1-f6 |
784.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.680735453$ |
1.357775030 |
\( \frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1562 a - 3681\) , \( 52607 a + 96844\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-1562a-3681\right){x}+52607a+96844$ |
*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.
