| 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 |
| 16.2-a2 |
16.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{13} \) |
$1.02666$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.74710193$ |
1.196531640 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( a\) , \( 130 a - 436\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}+130a-436$ |
| 16.2-b2 |
16.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{13} \) |
$1.02666$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.99543515$ |
2.175573380 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a - 8\) , \( -3 a - 8\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3a-8\right){x}-3a-8$ |
| 128.5-a2 |
128.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{19} \) |
$1.72662$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.116510987$ |
$16.87231618$ |
1.368814535 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -88 a - 209\) , \( -87 a - 207\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-88a-209\right){x}-87a-207$ |
| 128.5-h2 |
128.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( - 2^{19} \) |
$1.72662$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.18279859$ |
1.772597710 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 3 a + 7\) , \( 9 a - 17\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+7\right){x}+9a-17$ |
| 256.1-c2 |
256.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.260186307$ |
$12.49771757$ |
2.264217622 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -123 a - 288\) , \( 122 a + 288\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-123a-288\right){x}+122a+288$ |
| 256.1-h2 |
256.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.236354820$ |
$6.873550969$ |
2.262448170 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 32 a - 108\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+32a-108$ |
| 288.3-b2 |
288.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{6} \) |
$2.11468$ |
$(-a-2), (-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.128866509$ |
$14.43112121$ |
2.589841338 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 5\) , \( -a + 10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(2a+5\right){x}-a+10$ |
| 288.3-o2 |
288.3-o |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{6} \) |
$2.11468$ |
$(-a-2), (-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$7.936893005$ |
2.763271459 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -415 a - 987\) , \( -2231 a - 5294\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-415a-987\right){x}-2231a-5294$ |
| 512.4-i2 |
512.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{31} \) |
$2.44182$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.305737308$ |
$5.091399298$ |
2.314546963 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 3\) , \( 4963 a - 16738\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a-3\right){x}+4963a-16738$ |
| 512.4-l2 |
512.4-l |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
512.4 |
\( 2^{9} \) |
\( - 2^{31} \) |
$2.44182$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.436158092$ |
1.468546625 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -17 a - 40\) , \( -17 a - 40\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-17a-40\right){x}-17a-40$ |
*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.
