| 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 |
| 18.1-a8 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.531367511$ |
1.606704330 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 32558 a - 86161\) , \( 5180690 a - 13706875\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(32558a-86161\right){x}+5180690a-13706875$ |
| 18.1-b8 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 32558 a - 86158\) , \( -5180691 a + 13706871\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32558a-86158\right){x}-5180691a+13706871$ |
| 162.1-a8 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 293022 a - 775440\) , \( -140361053 a + 371361301\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(293022a-775440\right){x}-140361053a+371361301$ |
| 162.1-b8 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.177122503$ |
1.071136220 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 293022 a - 775440\) , \( 140361053 a - 371361301\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(293022a-775440\right){x}+140361053a-371361301$ |
| 432.1-b8 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.885572036$ |
$1.010534464$ |
2.968158376 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -399552 a - 1057344\) , \( 223692872 a + 591834184\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-399552a-1057344\right){x}+223692872a+591834184$ |
| 432.1-i8 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.372544023$ |
2.252934490 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -399552 a - 1057347\) , \( -224092424 a - 592891530\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-399552a-1057347\right){x}-224092424a-592891530$ |
| 432.2-b8 |
432.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.971393009$ |
$1.010534464$ |
2.968158376 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 53992 a - 144544\) , \( 11203576 a - 29616296\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(53992a-144544\right){x}+11203576a-29616296$ |
| 432.2-i8 |
432.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.372544023$ |
2.252934490 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 53990 a - 144547\) , \( -11149585 a + 29471750\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(53990a-144547\right){x}-11149585a+29471750$ |
*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.
