| 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 |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.210429933$ |
$7.027708105$ |
2.837608018 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 2821783 a - 13235292\) , \( -5606242215 a + 26295606899\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2821783a-13235292\right){x}-5606242215a+26295606899$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.893869405$ |
$7.027708105$ |
2.837608018 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 8623 a - 40402\) , \( 1902615 a - 8923995\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8623a-40402\right){x}+1902615a-8923995$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.631289801$ |
$7.027708105$ |
2.837608018 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -74117 a + 347683\) , \( -39870180 a + 187007781\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-74117a+347683\right){x}-39870180a+187007781$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.315644900$ |
$7.027708105$ |
2.837608018 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 587803 a - 2756997\) , \( -435913260 a + 2044614485\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(587803a-2756997\right){x}-435913260a+2044614485$ |
| 98.1-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.946934702$ |
$7.027708105$ |
2.837608018 |
\( \frac{128787625}{98} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 174103 a - 816572\) , \( 85448205 a - 400787547\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(174103a-816572\right){x}+85448205a-400787547$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.105214966$ |
$7.027708105$ |
2.837608018 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 45184663 a - 211934812\) , \( -358093996455 a + 1679609724531\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(45184663a-211934812\right){x}-358093996455a+1679609724531$ |
| 98.1-b1 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$25.04165481$ |
$0.436190660$ |
2.328777771 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 98.1-b2 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.782406090$ |
$35.33144352$ |
2.328777771 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 98.1-b3 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.782406090$ |
$3.925715946$ |
2.328777771 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 98.1-b4 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.695601522$ |
$3.925715946$ |
2.328777771 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 98.1-b5 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.695601522$ |
$35.33144352$ |
2.328777771 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 98.1-b6 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.63746$ |
$(-3a-14), (2a+9), (-2a+9)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$6.260413703$ |
$0.436190660$ |
2.328777771 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
*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.
