| 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 |
| 75.1-a6 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$0.45547$ |
$(-2a+1), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.322695746 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 1875.1-b6 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$1.01847$ |
$(-2a+1), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.223570171$ |
1.032626388 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$ |
| 11025.1-c6 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{22} \cdot 5^{4} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.243935055$ |
2.253375518 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2025 a + 1215\) , \( -37159 a + 66759\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2025a+1215\right){x}-37159a+66759$ |
| 11025.3-c6 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{22} \cdot 5^{4} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.243935055$ |
2.253375518 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1213 a - 2026\) , \( 33919 a + 30815\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1213a-2026\right){x}+33919a+30815$ |
| 12675.1-a6 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.310036044$ |
2.863990301 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1079 a + 2025\) , \( -21863 a - 9057\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1079a+2025\right){x}-21863a-9057$ |
| 12675.3-a6 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.310036044$ |
2.863990301 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2025 a + 1081\) , \( 22808 a - 32945\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2025a+1081\right){x}+22808a-32945$ |
| 19200.1-g6 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{16} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$2.600625687$ |
$0.279462714$ |
3.356843389 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2160{x}+37908$ |
| 57600.1-j6 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{22} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6480 a\) , \( -227448 a + 113724\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-6480a{x}-227448a+113724$ |
| 57600.1-k6 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{22} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6482 a - 6481\) , \( 233929 a - 120205\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6482a-6481\right){x}+233929a-120205$ |
| 81225.1-a6 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{22} \cdot 5^{4} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.027707458$ |
$0.148062962$ |
2.754442525 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2026 a - 6481\) , \( -104775 a - 192360\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2026a-6481\right){x}-104775a-192360$ |
| 81225.3-a6 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{22} \cdot 5^{4} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.027707458$ |
$0.148062962$ |
2.754442525 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 6481 a + 2025\) , \( 104774 a - 297134\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6481a+2025\right){x}+104774a-297134$ |
| 102675.1-a6 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$12.07263470$ |
$0.183773548$ |
5.123708641 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 945 a + 4456\) , \( 151963 a - 107681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(945a+4456\right){x}+151963a-107681$ |
| 102675.3-a6 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$12.07263470$ |
$0.183773548$ |
5.123708641 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 5401 a - 4456\) , \( -151963 a + 44282\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(5401a-4456\right){x}-151963a+44282$ |
*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.
