| 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 |
| 6272.2-a1 |
6272.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \) |
$1$ |
$0.954284139$ |
1.442742008 |
\( \frac{1221075}{8} a - \frac{1031913}{4} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 105 a - 80\) , \( -495 a + 17\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(105a-80\right){x}-495a+17$ |
| 6272.2-a2 |
6272.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \) |
$1$ |
$0.954284139$ |
1.442742008 |
\( \frac{3645}{64} a + \frac{32697}{32} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 46\) , \( -19 a + 73\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+46{x}-19a+73$ |
| 6272.2-b1 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{54} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$7.354422918$ |
$0.116982535$ |
2.601420732 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 5967 a + 2388\) , \( 30581 a - 379207\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5967a+2388\right){x}+30581a-379207$ |
| 6272.2-b2 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$1.225737153$ |
$0.350947606$ |
2.601420732 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -75 a - 926\) , \( -1431 a - 10998\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-75a-926\right){x}-1431a-10998$ |
| 6272.2-b3 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{33} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$1.225737153$ |
$0.350947606$ |
2.601420732 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -705 a + 613\) , \( 3295 a - 11977\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-705a+613\right){x}+3295a-11977$ |
| 6272.2-b4 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.408579051$ |
$1.052842818$ |
2.601420732 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -40 a - 17\) , \( -170 a + 77\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-40a-17\right){x}-170a+77$ |
| 6272.2-b5 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.408579051$ |
$1.052842818$ |
2.601420732 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -40 a - 16\) , \( 144 a - 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-40a-16\right){x}+144a-64$ |
| 6272.2-b6 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$0.817158102$ |
$1.052842818$ |
2.601420732 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 17 a + 8\) , \( -9 a + 109\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a+8\right){x}-9a+109$ |
| 6272.2-b7 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{12} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{5} \) |
$2.451474306$ |
$0.350947606$ |
2.601420732 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -158 a - 62\) , \( 201 a - 2495\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-158a-62\right){x}+201a-2495$ |
| 6272.2-b8 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{63} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.677211459$ |
$0.116982535$ |
2.601420732 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -110 a + 2644\) , \( -6716 a - 58360\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-110a+2644\right){x}-6716a-58360$ |
| 6272.2-b9 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{63} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.677211459$ |
$0.116982535$ |
2.601420732 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1780 a - 1977\) , \( 16700 a - 68439\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1780a-1977\right){x}+16700a-68439$ |
| 6272.2-b10 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{18} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$4.902948612$ |
$0.175473803$ |
2.601420732 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 1242 a + 498\) , \( 2441 a - 30271\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1242a+498\right){x}+2441a-30271$ |
| 6272.2-b11 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.634316204$ |
$0.526421409$ |
2.601420732 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 367 a + 148\) , \( -429 a + 5317\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(367a+148\right){x}-429a+5317$ |
| 6272.2-b12 |
6272.2-b |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$14.70884583$ |
$0.058491267$ |
2.601420732 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 95567 a + 38228\) , \( 1930101 a - 23933255\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(95567a+38228\right){x}+1930101a-23933255$ |
| 6272.2-c1 |
6272.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.887223600$ |
1.341356002 |
\( -\frac{16471}{4} a + \frac{2971}{4} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -57 a + 8\) , \( -201 a + 141\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57a+8\right){x}-201a+141$ |
| 6272.2-c2 |
6272.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.887223600$ |
1.341356002 |
\( \frac{16471}{4} a - 3375 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -35 a - 44\) , \( -227 a - 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-44\right){x}-227a-7$ |
| 6272.2-c3 |
6272.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{39} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.887223600$ |
1.341356002 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 5 a + 57\) , \( -49 a - 21\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(5a+57\right){x}-49a-21$ |
| 6272.2-c4 |
6272.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{39} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.887223600$ |
1.341356002 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 43 a - 37\) , \( -44 a + 38\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(43a-37\right){x}-44a+38$ |
| 6272.2-d1 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.517549865$ |
$0.522988206$ |
4.799608661 |
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -746 a + 896\) , \( 424 a - 14864\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-746a+896\right){x}+424a-14864$ |
| 6272.2-d2 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{11} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.035099730$ |
$1.045976412$ |
4.799608661 |
\( -\frac{13647889}{14} a - \frac{40536829}{7} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 66 a - 195\) , \( -471 a + 1026\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(66a-195\right){x}-471a+1026$ |
| 6272.2-d3 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.758774932$ |
$1.045976412$ |
4.799608661 |
\( -\frac{1145925}{112} a - \frac{72257}{56} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -46 a + 56\) , \( 4 a - 248\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-46a+56\right){x}+4a-248$ |
| 6272.2-d4 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{7} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.379387466$ |
$1.045976412$ |
4.799608661 |
\( -\frac{138325}{1792} a - \frac{317937}{896} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 18 a - 24\) , \( -92 a + 24\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(18a-24\right){x}-92a+24$ |
| 6272.2-d5 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{17} \cdot 7^{14} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.035099730$ |
$0.522988206$ |
4.799608661 |
\( -\frac{5786513}{4802} a + \frac{263001}{343} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -39 a - 135\) , \( 23 a + 957\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-39a-135\right){x}+23a+957$ |
| 6272.2-d6 |
6272.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{10} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.517549865$ |
$1.045976412$ |
4.799608661 |
\( \frac{361845}{196} a - \frac{43727}{98} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 31 a + 5\) , \( 37 a + 89\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(31a+5\right){x}+37a+89$ |
| 6272.2-e1 |
6272.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{15} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.203676363$ |
$2.524798514$ |
4.664762970 |
\( \frac{1221075}{8} a - \frac{1031913}{4} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -14 a + 12\) , \( -4 a + 24\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+12\right){x}-4a+24$ |
| 6272.2-e2 |
6272.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.101838181$ |
$2.524798514$ |
4.664762970 |
\( \frac{3645}{64} a + \frac{32697}{32} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( a - 6\) , \( 5 a + 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-6\right){x}+5a+2$ |
| 6272.2-f1 |
6272.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.347373005$ |
3.548894403 |
\( -\frac{16471}{4} a + \frac{2971}{4} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 2\) , \( 7 a + 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-2\right){x}+7a+6$ |
| 6272.2-f2 |
6272.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{3} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.2[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$2.347373005$ |
3.548894403 |
\( \frac{16471}{4} a - 3375 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 5 a + 7\) , \( -9 a + 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(5a+7\right){x}-9a+18$ |
| 6272.2-f3 |
6272.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{39} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.335339000$ |
3.548894403 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -31 a - 402\) , \( 237 a - 1054\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-402\right){x}+237a-1054$ |
| 6272.2-f4 |
6272.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6272.2 |
\( 2^{7} \cdot 7^{2} \) |
\( 2^{39} \cdot 7^{9} \) |
$2.10397$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.6.1[2] |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$0.335339000$ |
3.548894403 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -305 a + 267\) , \( -219 a - 962\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-305a+267\right){x}-219a-962$ |
*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.
