| 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 |
| 146523.2-a1 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 13^{16} \cdot 17^{2} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.629377867$ |
$0.198460595$ |
4.615354918 |
\( \frac{1193377118543}{124806800313} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 221\) , \( 17042\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+221{x}+17042$ |
| 146523.2-a2 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 13^{2} \cdot 17^{16} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.517511471$ |
$0.099230297$ |
4.615354918 |
\( \frac{6439735268725823}{7345472585373} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3876\) , \( -89910\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3876{x}-89910$ |
| 146523.2-a3 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 13^{4} \cdot 17^{8} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.517511471$ |
$0.198460595$ |
4.615354918 |
\( \frac{296380748763217}{92608836489} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1389\) , \( -14094\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1389{x}-14094$ |
| 146523.2-a4 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 13^{8} \cdot 17^{4} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.517511471$ |
$0.396921190$ |
4.615354918 |
\( \frac{17806161424897}{668584449} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -544\) , \( 4496\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-544{x}+4496$ |
| 146523.2-a5 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{32} \cdot 13^{2} \cdot 17^{4} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$10.07004588$ |
$0.099230297$ |
4.615354918 |
\( \frac{908031902324522977}{161726530797} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -20174\) , \( -1111138\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-20174{x}-1111138$ |
| 146523.2-a6 |
146523.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 13^{4} \cdot 17^{2} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.517511471$ |
$0.793842381$ |
4.615354918 |
\( \frac{17319700013617}{25857} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -539\) , \( 4592\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-539{x}+4592$ |
| 146523.2-b1 |
146523.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{24} \cdot 13^{2} \cdot 17^{4} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.385394292$ |
1.780059986 |
\( \frac{3885442650361}{1996623837} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 327 a\) , \( -900\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+327a{x}-900$ |
| 146523.2-b2 |
146523.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{12} \cdot 13^{4} \cdot 17^{2} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.770788584$ |
1.780059986 |
\( \frac{2000852317801}{2094417} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 262 a\) , \( -1745\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+262a{x}-1745$ |
| 146523.2-c1 |
146523.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 13^{2} \cdot 17^{4} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.204192024$ |
$0.771211323$ |
2.909387201 |
\( \frac{104154702625}{24649677} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 98 a\) , \( 279\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+98a{x}+279$ |
| 146523.2-c2 |
146523.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146523.2 |
\( 3 \cdot 13^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 13^{4} \cdot 17^{2} \) |
$3.02814$ |
$(-2a+1), (-4a+1), (4a-3), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.102096012$ |
$1.542422646$ |
2.909387201 |
\( \frac{3981876625}{232713} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 33 a\) , \( -72\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+33a{x}-72$ |
*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.
