| 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 |
| 16.1-CMa1 |
16.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -3375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$ |
| 16.1-CMa2 |
16.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.270482382$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a + 11\) , \( -7 a + 26\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+11\right){x}-7a+26$ |
| 16.5-CMa1 |
16.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -3375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$ |
| 16.5-CMa2 |
16.5-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16.5 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.47284$ |
$(-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.270482382$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 5\) , \( 22 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-5\right){x}+22a+14$ |
| 28.2-a1 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.875417135$ |
0.330876576 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 28.2-a2 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{15} \cdot 7^{3} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.330876576 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -10 a + 15\) , \( -5 a - 16\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-10a+15\right){x}-5a-16$ |
| 28.2-a3 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{15} \cdot 7^{3} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.330876576 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 9 a + 6\) , \( 4 a - 20\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+6\right){x}+4a-20$ |
| 28.2-a4 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{5} \cdot 7 \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.330876576 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 1\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a+1$ |
| 28.2-a5 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{5} \cdot 7 \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.330876576 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}$ |
| 28.2-a6 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$7.878754216$ |
0.330876576 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 28.2-a7 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.626251405$ |
0.330876576 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 28.2-a8 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{45} \cdot 7 \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.330876576 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 30 a - 40\) , \( -30 a - 154\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(30a-40\right){x}-30a-154$ |
| 28.2-a9 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{45} \cdot 7 \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.330876576 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -31 a - 9\) , \( 29 a - 183\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-9\right){x}+29a-183$ |
| 28.2-a10 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.330876576 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 28.2-a11 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.330876576 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 28.2-a12 |
28.2-a |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$0.54385$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.330876576 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 44.3-a1 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( \frac{2775668240489}{85184} a - \frac{3929396676037}{42592} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -55 a + 91\) , \( 87 a + 359\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-55a+91\right){x}+87a+359$ |
| 44.3-a2 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{7} \cdot 11^{12} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.840444112$ |
0.635316032 |
\( -\frac{41728910180660407}{200859416110144} a - \frac{5044929390482523}{100429708055072} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -4 a + 40\) , \( 135 a + 83\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4a+40\right){x}+135a+83$ |
| 44.3-a3 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{2222449}{45056} a + \frac{42043605}{45056} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$ |
| 44.3-a4 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{25} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( -\frac{74168468086089}{22330474496} a + \frac{45400743717419}{11165237248} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 14 a - 17\) , \( -19 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-17\right){x}-19a+5$ |
| 44.3-a5 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( -\frac{998361}{7744} a + \frac{23448551}{7744} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( a\) , \( 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}+1$ |
| 44.3-a6 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11^{6} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( \frac{49453830610989}{7256313856} a - \frac{991801247255}{3628156928} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -14 a - 10\) , \( 27 a - 9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14a-10\right){x}+27a-9$ |
| 44.3-a7 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{11} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{7153263}{2816} a + \frac{40910099}{1408} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( -3 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+3\right){x}-3a+1$ |
| 44.3-a8 |
44.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \) |
$0.60891$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.521332337$ |
0.635316032 |
\( -\frac{67333244623}{117128} a + \frac{557731279327}{117128} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 21 a\) , \( 20 a + 57\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+21a{x}+20a+57$ |
| 44.4-a1 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( -\frac{2775668240489}{85184} a - \frac{5083125111585}{85184} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 55 a + 36\) , \( -87 a + 446\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(55a+36\right){x}-87a+446$ |
| 44.4-a2 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{7} \cdot 11^{12} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.840444112$ |
0.635316032 |
\( \frac{41728910180660407}{200859416110144} a - \frac{51818768961625453}{200859416110144} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 3 a + 37\) , \( -136 a + 219\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3a+37\right){x}-136a+219$ |
| 44.4-a3 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( -\frac{2222449}{45056} a + \frac{22133027}{22528} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}+1$ |
| 44.4-a4 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{25} \cdot 11^{3} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( \frac{74168468086089}{22330474496} a + \frac{16633019348749}{22330474496} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -14 a - 3\) , \( 19 a - 14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-14a-3\right){x}+19a-14$ |
| 44.4-a5 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( \frac{998361}{7744} a + \frac{11225095}{3872} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -2 a + 2\) , \( -a + 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a+2\right){x}-a+2$ |
| 44.4-a6 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{14} \cdot 11^{6} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.680888225$ |
0.635316032 |
\( -\frac{49453830610989}{7256313856} a + \frac{47470228116479}{7256313856} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 13 a - 23\) , \( -28 a + 19\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(13a-23\right){x}-28a+19$ |
| 44.4-a7 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{11} \cdot 11 \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.042664675$ |
0.635316032 |
\( -\frac{7153263}{2816} a + \frac{88973461}{2816} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( a + 2\) , \( 3 a - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}+3a-2$ |
| 44.4-a8 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.521332337$ |
0.635316032 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -22 a + 22\) , \( -21 a + 78\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-22a+22\right){x}-21a+78$ |
| 46.2-a1 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{2} \cdot 23 \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( -\frac{13982353}{92} a - \frac{23126489}{92} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-1$ |
| 46.2-a2 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{2} \cdot 23^{4} \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.250037765$ |
0.614199405 |
\( \frac{77942691519}{1119364} a - \frac{145858368769}{1119364} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -6 a + 10\) , \( 2 a + 8\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+10\right){x}+2a+8$ |
| 46.2-a3 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2 \cdot 23^{8} \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.625018882$ |
0.614199405 |
\( \frac{5221695638593}{156621970562} a + \frac{45422616717183}{156621970562} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -a + 10\) , \( -8 a + 30\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+10\right){x}-8a+30$ |
| 46.2-a4 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{4} \cdot 23^{2} \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( -\frac{1695309}{8464} a + \frac{8874095}{8464} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$ |
| 46.2-a5 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{8} \cdot 23 \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( \frac{2993221}{5888} a + \frac{15291513}{5888} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 2\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}-a+1$ |
| 46.2-a6 |
46.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2 \cdot 23^{2} \) |
$0.61571$ |
$(a), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.625018882$ |
0.614199405 |
\( -\frac{14178949136401}{1058} a + \frac{7909975811569}{1058} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -91 a + 170\) , \( 240 a + 618\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-91a+170\right){x}+240a+618$ |
| 46.3-a1 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2^{2} \cdot 23 \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( \frac{13982353}{92} a - \frac{18554421}{46} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( a - 4\) , \( -a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-4\right){x}-a-4$ |
| 46.3-a2 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2^{2} \cdot 23^{4} \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.250037765$ |
0.614199405 |
\( -\frac{77942691519}{1119364} a - \frac{33957838625}{559682} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 5 a + 4\) , \( -3 a + 10\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+4\right){x}-3a+10$ |
| 46.3-a3 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2 \cdot 23^{8} \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.625018882$ |
0.614199405 |
\( -\frac{5221695638593}{156621970562} a + \frac{25322156177888}{78310985281} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 9\) , \( 7 a + 22\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+9{x}+7a+22$ |
| 46.3-a4 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2^{4} \cdot 23^{2} \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( \frac{1695309}{8464} a + \frac{3589393}{4232} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-{x}-a$ |
| 46.3-a5 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2^{8} \cdot 23 \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.500075531$ |
0.614199405 |
\( -\frac{2993221}{5888} a + \frac{9142367}{2944} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -2\) , \( 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-2{x}+1$ |
| 46.3-a6 |
46.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2 \cdot 23^{2} \) |
$0.61571$ |
$(-a+1), (-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.625018882$ |
0.614199405 |
\( \frac{14178949136401}{1058} a - \frac{3134486662416}{529} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 90 a + 79\) , \( -241 a + 858\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(90a+79\right){x}-241a+858$ |
| 49.1-CMa1 |
49.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$0.62551$ |
$(-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.1.4[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$4.944504600$ |
0.934423537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$ |
| 49.1-CMa2 |
49.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$0.62551$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$2.472252300$ |
0.934423537 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$ |
| 63.1-a1 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.862076929$ |
0.325834452 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 63.1-a2 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.896615437$ |
0.325834452 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 63.1-a3 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.448307718$ |
0.325834452 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 63.1-a4 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.724153859$ |
0.325834452 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
*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.
