| 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-a6 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.647145070$ |
0.747258760 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 7500.1-b6 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{24} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.129429014$ |
1.793421026 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8337 a\) , \( -295969\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+8337a{x}-295969$ |
| 19200.1-e6 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 5^{12} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.161786267$ |
2.241776282 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5336\) , \( 151536\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5336{x}+151536$ |
| 44100.1-b6 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{12} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.141218631$ |
1.956782763 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5005 a + 3001\) , \( -134060 a + 257817\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5005a+3001\right){x}-134060a+257817$ |
| 44100.3-b6 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{12} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.141218631$ |
1.956782763 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -3002 a - 5003\) , \( 142065 a + 120755\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3002a-5003\right){x}+142065a+120755$ |
| 50700.1-b6 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.286467203$ |
$0.179485748$ |
2.724511424 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5002 a - 2335\) , \( -85239 a - 40252\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5002a-2335\right){x}-85239a-40252$ |
| 50700.3-b6 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$3.286467203$ |
$0.179485748$ |
2.724511424 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -5003 a + 2668\) , \( 85239 a - 125491\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5003a+2668\right){x}+85239a-125491$ |
| 57600.1-a6 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{10} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$8.562837774$ |
$0.093407345$ |
3.694265501 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -16008 a\) , \( 909216 a - 454608\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-16008a{x}+909216a-454608$ |
| 57600.1-p6 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{10} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B[2] |
$1$ |
\( 2^{5} \) |
$8.562837774$ |
$0.093407345$ |
3.694265501 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -16008 a\) , \( -909216 a + 454608\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-16008a{x}-909216a+454608$ |
*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.
