| 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 |
| 300.1-a3 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.323572535$ |
0.747258760 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 7500.1-b3 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.064714507$ |
1.793421026 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 11337 a\) , \( -67969\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+11337a{x}-67969$ |
| 19200.1-e3 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{2} \cdot 5^{24} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.080893133$ |
2.241776282 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7256\) , \( 34800\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7256{x}+34800$ |
| 44100.1-b3 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{24} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.070609315$ |
1.956782763 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6805 a + 4081\) , \( -21740 a + 53553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6805a+4081\right){x}-21740a+53553$ |
| 44100.3-b3 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{24} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.070609315$ |
1.956782763 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -4082 a - 6803\) , \( 32625 a + 27731\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4082a-6803\right){x}+32625a+27731$ |
| 50700.1-b3 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 6802 a - 3175\) , \( -19575 a - 9244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(6802a-3175\right){x}-19575a-9244$ |
| 50700.3-b3 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$6.572934406$ |
$0.089742874$ |
2.724511424 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -6803 a + 3628\) , \( 19575 a - 28819\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6803a+3628\right){x}+19575a-28819$ |
| 57600.1-a3 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 5^{24} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$4.281418887$ |
$0.046703672$ |
3.694265501 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -21768 a\) , \( 208800 a - 104400\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-21768a{x}+208800a-104400$ |
| 57600.1-p3 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 5^{24} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$4.281418887$ |
$0.046703672$ |
3.694265501 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -21768 a\) , \( -208800 a + 104400\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-21768a{x}-208800a+104400$ |
*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.
