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 |
2.1-c6 |
2.1-c |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$2.71558$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$17.67811169$ |
1.305911907 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 5\) , \( -168562107136250046 a^{2} - 255910771809962227 a + 535500577238303301\) , \( -61353841318711367560260837 a^{2} - 93147322088742339719223147 a + 194913423901376825030234481\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-168562107136250046a^{2}-255910771809962227a+535500577238303301\right){x}-61353841318711367560260837a^{2}-93147322088742339719223147a+194913423901376825030234481$ |
16.3-f2 |
16.3-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{14} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.629352769$ |
0.341978091 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -16243 a^{2} - 24656 a + 51597\) , \( -1816294 a^{2} - 2757459 a + 5770094\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-16243a^{2}-24656a+51597\right){x}-1816294a^{2}-2757459a+5770094$ |
50.2-f4 |
50.2-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( - 2^{2} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$26.35925859$ |
3.894405722 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -29536239227733795051 a^{2} - 44841879978537109382 a + 93832910756836507680\) , \( -142309740288908754264404174212 a^{2} - 216054462608090711628571981567 a + 452100115299015591863821852949\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29536239227733795051a^{2}-44841879978537109382a+93832910756836507680\right){x}-142309740288908754264404174212a^{2}-216054462608090711628571981567a+452100115299015591863821852949$ |
64.4-e6 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.373398606$ |
$55.50090546$ |
2.296370864 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( -3292327 a^{2} - 4998407 a + 10459320\) , \( 5296745678 a^{2} + 8041512394 a - 16827093684\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3292327a^{2}-4998407a+10459320\right){x}+5296745678a^{2}+8041512394a-16827093684$ |
64.4-j4 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$29.06795419$ |
0.536824692 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -1428386 a^{2} - 2168574 a + 4537804\) , \( 1511760684 a^{2} + 2295153105 a - 4802673228\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-1428386a^{2}-2168574a+4537804\right){x}+1511760684a^{2}+2295153105a-4802673228$ |
98.2-h2 |
98.2-h |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( - 2^{2} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.499461759$ |
2.068089108 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( a\) , \( -11830738379586025598 a^{2} - 17961411619957731685 a + 37584765277659585008\) , \( -36076102052309870146954656095 a^{2} - 54770691212581199665160384273 a + 114609230993442438745707389772\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-11830738379586025598a^{2}-17961411619957731685a+37584765277659585008\right){x}-36076102052309870146954656095a^{2}-54770691212581199665160384273a+114609230993442438745707389772$ |
*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.