| 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-c5 |
2.1-c |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$2.71558$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$141.4248935$ |
1.305911907 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 5\) , \( -44174316128285721 a^{2} - 67065389289594007 a + 140336236819129681\) , \( 8484866098384540422058642 a^{2} + 12881712674525578166721139 a - 26955350586605825705197871\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-44174316128285721a^{2}-67065389289594007a+140336236819129681\right){x}+8484866098384540422058642a^{2}+12881712674525578166721139a-26955350586605825705197871$ |
| 16.3-f1 |
16.3-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{16} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$37.03482215$ |
0.341978091 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -4258 a^{2} - 6456 a + 13517\) , \( 258740 a^{2} + 392840 a - 822010\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4258a^{2}-6456a+13517\right){x}+258740a^{2}+392840a-822010$ |
| 50.2-f3 |
50.2-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$105.4370343$ |
3.894405722 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -7740429869163610016 a^{2} - 11751510559590955497 a + 24590370477863559860\) , \( 19680578595356447217577587270 a^{2} + 29879028825459992749221495373 a - 62522718642087515259755834219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7740429869163610016a^{2}-11751510559590955497a+24590370477863559860\right){x}+19680578595356447217577587270a^{2}+29879028825459992749221495373a-62522718642087515259755834219$ |
| 64.4-e5 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{22} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.746797212$ |
$111.0018109$ |
2.296370864 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( -862807 a^{2} - 1309912 a + 2741040\) , \( -732248066 a^{2} - 1111698063 a + 2326259844\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-862807a^{2}-1309912a+2741040\right){x}-732248066a^{2}-1111698063a+2326259844$ |
| 64.4-j3 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{22} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$58.13590838$ |
0.536824692 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -374331 a^{2} - 568309 a + 1189204\) , \( -209746460 a^{2} - 318436802 a + 666338076\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-374331a^{2}-568309a+1189204\right){x}-209746460a^{2}-318436802a+666338076$ |
| 98.2-h1 |
98.2-h |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$27.99569407$ |
2.068089108 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( a\) , \( -3100428596258839498 a^{2} - 4707066662194364530 a + 9849671027431644628\) , \( 4989107280129669939057958946 a^{2} + 7574456183492445598473896895 a - 15849765251532649321098355880\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-3100428596258839498a^{2}-4707066662194364530a+9849671027431644628\right){x}+4989107280129669939057958946a^{2}+7574456183492445598473896895a-15849765251532649321098355880$ |
*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.
