| 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 |
| 1026.1-a1 |
1026.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{9} \cdot 3^{11} \cdot 19 \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.060069731$ |
$0.810514802$ |
1.215095416 |
\( -\frac{103295563555}{608} a - \frac{11571663473}{76} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -235 a - 340\) , \( -2616 a - 1480\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-235a-340\right){x}-2616a-1480$ |
| 1026.1-a2 |
1026.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2 \cdot 3^{3} \cdot 19 \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.060069731$ |
$7.294633218$ |
1.215095416 |
\( \frac{39341}{38} a - \frac{70124}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}$ |
| 1026.1-a3 |
1026.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{3} \cdot 3^{9} \cdot 19^{3} \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$0.353356577$ |
$2.431544406$ |
1.215095416 |
\( -\frac{3536645}{27436} a + \frac{10111198}{6859} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -5 a - 5\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-5a-5\right){x}-a-2$ |
| 1026.1-b1 |
1026.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{5} \cdot 3^{9} \cdot 19^{2} \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.017402832$ |
$2.800235056$ |
2.067524558 |
\( -\frac{246375}{2888} a - \frac{158625}{1444} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -a - 4\) , \( a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-4\right){x}+a+5$ |
| 1026.1-c1 |
1026.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{19} \cdot 3^{9} \cdot 19 \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \cdot 19 \) |
$0.024585501$ |
$1.455655769$ |
2.884879096 |
\( \frac{8148789}{19456} a - \frac{31326021}{4864} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -5 a + 28\) , \( -34 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a+28\right){x}-34a-11$ |
| 1026.1-d1 |
1026.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2 \cdot 3^{9} \cdot 19^{2} \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.640310313$ |
2.716606587 |
\( -\frac{16703412222599}{722} a - \frac{15471414698461}{361} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -360 a + 1114\) , \( 8828 a + 10097\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-360a+1114\right){x}+8828a+10097$ |
| 1026.1-d2 |
1026.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{3} \cdot 3^{3} \cdot 19^{6} \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.920930939$ |
2.716606587 |
\( -\frac{365593536355}{188183524} a + \frac{313233427909}{94091762} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -5 a + 14\) , \( 4 a + 17\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+14\right){x}+4a+17$ |
| 1026.1-d3 |
1026.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1026.1 |
\( 2 \cdot 3^{3} \cdot 19 \) |
\( 2^{9} \cdot 3^{5} \cdot 19^{2} \) |
$1.43044$ |
$(a), (-a-1), (-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.920930939$ |
2.716606587 |
\( \frac{12298987609}{11552} a + \frac{1200903779}{5776} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -20 a - 35\) , \( -73 a - 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-20a-35\right){x}-73a-55$ |
*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.
