| 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 |
| 4802.1-a1 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{36} \cdot 7^{14} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -8355\) , \( 291341\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-8355{x}+291341$ |
| 4802.1-a2 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-25{x}-111$ |
| 4802.1-a3 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{12} \cdot 7^{18} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+220{x}+2192$ |
| 4802.1-a4 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{6} \cdot 7^{24} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1740{x}+22184$ |
| 4802.1-a5 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{2} \cdot 7^{16} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-515{x}-4717$ |
| 4802.1-a6 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{18} \cdot 7^{16} \) |
$2.57682$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.003958300$ |
2.318542380 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-133795{x}+18781197$ |
| 4802.1-b1 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{36} \cdot 7^{14} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.507207167$ |
$0.062312951$ |
4.542360682 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -8356\) , \( -299697\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-8356{x}-299697$ |
| 4802.1-b2 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.389689685$ |
$5.047349074$ |
4.542360682 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -26\) , \( 85\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-26{x}+85$ |
| 4802.1-b3 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{12} \cdot 7^{18} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.169069055$ |
$0.560816563$ |
4.542360682 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 219\) , \( -1973\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+219{x}-1973$ |
| 4802.1-b4 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{6} \cdot 7^{24} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.338138111$ |
$0.560816563$ |
4.542360682 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1741\) , \( -23925\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1741{x}-23925$ |
| 4802.1-b5 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{2} \cdot 7^{16} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.779379370$ |
$5.047349074$ |
4.542360682 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -516\) , \( 4201\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-516{x}+4201$ |
| 4802.1-b6 |
4802.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{18} \cdot 7^{16} \) |
$2.57682$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$7.014414334$ |
$0.062312951$ |
4.542360682 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -133796\) , \( -18914993\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-133796{x}-18914993$ |
*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.
