| 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 |
| 128.1-a1 |
128.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( 2^{8} \) |
$1.04119$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.09117728$ |
1.600873547 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}-1$ |
| 128.1-d1 |
128.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
128.1 |
\( 2^{7} \) |
\( 2^{8} \) |
$1.04119$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.142100224$ |
$27.22522842$ |
1.116800688 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}+1$ |
| 256.1-a1 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.23820$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$27.22522842$ |
1.964811619 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a+2\right){x}$ |
| 256.1-b1 |
256.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.23820$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$11.09117728$ |
0.800436773 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+2\right){x}$ |
| 1024.1-a1 |
1024.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.06626753$ |
2.463303538 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2{x}$ |
| 1024.1-b1 |
1024.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.381218488$ |
$8.846686439$ |
3.527381188 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 3\) , \( -4 a - 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2a-3\right){x}-4a-7$ |
| 1024.1-s1 |
1024.1-s |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.846686439$ |
1.276909199 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2{x}$ |
| 1024.1-t1 |
1024.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.399627251$ |
$17.06626753$ |
1.968806443 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 3\) , \( 4 a + 7\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2a-3\right){x}+4a+7$ |
| 1152.1-h1 |
1152.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1152.1 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.80340$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.345131123$ |
$13.93454908$ |
2.776619808 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-3a+6\right){x}$ |
| 1152.1-j1 |
1152.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1152.1 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.80340$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.223289230$ |
2.085183990 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-3a+6\right){x}$ |
| 2304.1-bc1 |
2304.1-bc |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.223289230$ |
1.042591995 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-a{x}-a-1$ |
| 2304.1-bf1 |
2304.1-bf |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.93454908$ |
2.011278916 |
\( -512 a + 512 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-a{x}+a+1$ |
*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.
