| 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 |
| 3528.1-a1 |
3528.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{4} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.738222370$ |
$4.730357929$ |
4.032278992 |
\( \frac{11664}{49} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -9 a + 18\) , \( 57 a - 98\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a+18\right){x}+57a-98$ |
| 3528.1-a2 |
3528.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.369111185$ |
$9.460715858$ |
4.032278992 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( -5\bigr] \) |
${y}^2={x}^{3}-6{x}-5$ |
| 3528.1-b1 |
3528.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.163487024$ |
2.498179631 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( -9\bigr] \) |
${y}^2={x}^{3}-6{x}-9$ |
| 3528.1-b2 |
3528.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.326974048$ |
2.498179631 |
\( \frac{21882096}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 111 a - 192\) , \( 747 a - 1296\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(111a-192\right){x}+747a-1296$ |
| 3528.1-c1 |
3528.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.714131080$ |
1.567004310 |
\( \frac{160917}{7} a - \frac{278433}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 8 a + 13\) , \( 115 a + 199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a+13\right){x}+115a+199$ |
| 3528.1-d1 |
3528.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.498576556$ |
$6.296527863$ |
3.624952765 |
\( \frac{160917}{7} a - \frac{278433}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 9 a + 15\) , \( -102 a - 173\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a+15\right){x}-102a-173$ |
| 3528.1-e1 |
3528.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.257561760$ |
$12.25657707$ |
3.645188179 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 9\bigr] \) |
${y}^2={x}^{3}-6{x}+9$ |
| 3528.1-e2 |
3528.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.128780880$ |
$24.51315415$ |
3.645188179 |
\( \frac{21882096}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 110 a - 194\) , \( -941 a + 1628\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(110a-194\right){x}-941a+1628$ |
| 3528.1-f1 |
3528.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.714131080$ |
1.567004310 |
\( -\frac{160917}{7} a - \frac{278433}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -9 a + 15\) , \( -102 a + 173\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a+15\right){x}-102a+173$ |
| 3528.1-g1 |
3528.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.498576556$ |
$6.296527863$ |
3.624952765 |
\( -\frac{160917}{7} a - \frac{278433}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10 a + 13\) , \( 115 a - 201\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a+13\right){x}+115a-201$ |
| 3528.1-h1 |
3528.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{4} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.212190782$ |
$9.430785234$ |
4.621401846 |
\( \frac{11664}{49} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10 a + 16\) , \( -41 a + 70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a+16\right){x}-41a+70$ |
| 3528.1-h2 |
3528.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3528.1 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.053047695$ |
$18.86157046$ |
4.621401846 |
\( \frac{55296}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 5\bigr] \) |
${y}^2={x}^{3}-6{x}+5$ |
*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.
