| 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-a1 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.294290140$ |
0.747258760 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 7500.1-b1 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{18} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.258858028$ |
1.793421026 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 337 a\) , \( -7969\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+337a{x}-7969$ |
| 19200.1-e1 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{48} \cdot 3^{2} \cdot 5^{6} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.323572535$ |
2.241776282 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 4080\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-216{x}+4080$ |
| 44100.1-b1 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{6} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.282437263$ |
1.956782763 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 205 a + 121\) , \( -3500 a + 6873\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(205a+121\right){x}-3500a+6873$ |
| 44100.3-b1 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{6} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.282437263$ |
1.956782763 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -122 a - 203\) , \( 3825 a + 3251\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-122a-203\right){x}+3825a+3251$ |
| 50700.1-b1 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.643233601$ |
$0.358971497$ |
2.724511424 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 202 a - 95\) , \( -2295 a - 1084\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(202a-95\right){x}-2295a-1084$ |
| 50700.3-b1 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.643233601$ |
$0.358971497$ |
2.724511424 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -203 a + 108\) , \( 2295 a - 3379\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-203a+108\right){x}+2295a-3379$ |
| 57600.1-a1 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{48} \cdot 3^{8} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$4.281418887$ |
$0.186814690$ |
3.694265501 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -648 a\) , \( 24480 a - 12240\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-648a{x}+24480a-12240$ |
| 57600.1-p1 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{48} \cdot 3^{8} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$4.281418887$ |
$0.186814690$ |
3.694265501 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -648 a\) , \( -24480 a + 12240\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-648a{x}-24480a+12240$ |
*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.
