| 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-a7 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.970717605$ |
0.747258760 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -289 a + 288\) , \( 1862\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-289a+288\right){x}+1862$ |
| 7500.1-b7 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{20} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \) |
$1$ |
$0.194143521$ |
1.793421026 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -7213\) , \( 232781\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-7213{x}+232781$ |
| 19200.1-e7 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{5} \) |
$1$ |
$0.242679401$ |
2.241776282 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4616\) , \( -119184\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4616{x}-119184$ |
| 44100.1-b7 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{8} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1$ |
$0.211827947$ |
1.956782763 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4330 a + 2596\) , \( 118660 a - 211038\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4330a+2596\right){x}+118660a-211038$ |
| 44100.3-b7 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{8} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1$ |
$0.211827947$ |
1.956782763 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -2597 a - 4328\) , \( -111735 a - 94975\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2597a-4328\right){x}-111735a-94975$ |
| 50700.1-b7 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 4327 a - 2020\) , \( 67041 a + 31658\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(4327a-2020\right){x}+67041a+31658$ |
| 50700.3-b7 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.190978135$ |
$0.269228623$ |
2.724511424 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4328 a + 2308\) , \( -67041 a + 98699\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4328a+2308\right){x}-67041a+98699$ |
| 57600.1-a7 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{12} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.427139629$ |
$0.140111017$ |
3.694265501 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -13848 a\) , \( -715104 a + 357552\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-13848a{x}-715104a+357552$ |
| 57600.1-p7 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{12} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.427139629$ |
$0.140111017$ |
3.694265501 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -13848 a\) , \( 715104 a - 357552\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-13848a{x}+715104a-357552$ |
*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.
