| 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 |
| 847.2-a1 |
847.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{2} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.098027979$ |
$4.822573867$ |
1.429453083 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+2{x}$ |
| 847.2-b1 |
847.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{2} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.803987222$ |
0.606082737 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$ |
| 847.2-b2 |
847.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{12} \cdot 11^{6} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.601329074$ |
0.606082737 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$ |
| 847.2-b3 |
847.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{18} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
0.606082737 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 847.2-c1 |
847.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{3} \cdot 11^{5} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.740150905$ |
$2.375448597$ |
2.658134078 |
\( -\frac{62743701596}{717409} a + \frac{29909553353}{717409} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 12 a - 19\) , \( -27 a + 9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(12a-19\right){x}-27a+9$ |
| 847.2-c2 |
847.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{3} \cdot 11^{5} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.740150905$ |
$2.375448597$ |
2.658134078 |
\( \frac{62743701596}{717409} a - \frac{32834148243}{717409} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -13 a - 6\) , \( 26 a - 17\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13a-6\right){x}+26a-17$ |
| 847.2-c3 |
847.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{6} \cdot 11^{4} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.480301811$ |
$2.375448597$ |
2.658134078 |
\( \frac{4657463}{41503} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}+11$ |
| 847.2-c4 |
847.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
847.2 |
\( 7 \cdot 11^{2} \) |
\( 7^{12} \cdot 11^{2} \) |
$1.27544$ |
$(-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.960603622$ |
$1.187724298$ |
2.658134078 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-51{x}+110$ |
*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.
