| 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-a5 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.941435210$ |
0.747258760 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -19 a + 18\) , \( 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-19a+18\right){x}+26$ |
| 7500.1-b5 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{16} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \) |
$1$ |
$0.388287042$ |
1.793421026 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -463\) , \( 3281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-463{x}+3281$ |
| 19200.1-e5 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{12} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \) |
$1$ |
$0.485358802$ |
2.241776282 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -296\) , \( -1680\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-296{x}-1680$ |
| 44100.1-b5 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \) |
$1$ |
$0.423655895$ |
1.956782763 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 280 a + 166\) , \( 2020 a - 3192\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(280a+166\right){x}+2020a-3192$ |
| 44100.3-b5 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \) |
$1$ |
$0.423655895$ |
1.956782763 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -167 a - 278\) , \( -1575 a - 1339\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-167a-278\right){x}-1575a-1339$ |
| 50700.1-b5 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.095489067$ |
$0.538457246$ |
2.724511424 |
\( \frac{702595369}{72900} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 277 a - 130\) , \( 945 a + 446\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(277a-130\right){x}+945a+446$ |
| 50700.3-b5 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$1.095489067$ |
$0.538457246$ |
2.724511424 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -278 a + 148\) , \( -945 a + 1391\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-278a+148\right){x}-945a+1391$ |
| 57600.1-a5 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{18} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$2.854279258$ |
$0.280222035$ |
3.694265501 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -888 a\) , \( -10080 a + 5040\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-888a{x}-10080a+5040$ |
| 57600.1-p5 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{18} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$2.854279258$ |
$0.280222035$ |
3.694265501 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -888 a\) , \( 10080 a - 5040\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-888a{x}+10080a-5040$ |
*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.
