| 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-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
0.322695746 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 1875.1-b5 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{16} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.894280685$ |
1.032626388 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$ |
| 11025.1-c5 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.975740221$ |
2.253375518 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 75 a + 45\) , \( 221 a - 483\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(75a+45\right){x}+221a-483$ |
| 11025.3-c5 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.975740221$ |
2.253375518 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -43 a - 76\) , \( -341 a - 217\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-76\right){x}-341a-217$ |
| 12675.1-a5 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.240144178$ |
2.863990301 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -39 a + 75\) , \( 149 a + 117\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-39a+75\right){x}+149a+117$ |
| 12675.3-a5 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.240144178$ |
2.863990301 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -75 a + 41\) , \( -114 a + 191\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-75a+41\right){x}-114a+191$ |
| 19200.1-g5 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.650156421$ |
$1.117850856$ |
3.356843389 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -300\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-80{x}-300$ |
| 57600.1-j5 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.332330370$ |
$0.645391492$ |
3.971591054 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -240 a\) , \( 1800 a - 900\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-240a{x}+1800a-900$ |
| 57600.1-k5 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.332330370$ |
$0.645391492$ |
3.971591054 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 242 a - 241\) , \( -1559 a + 659\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(242a-241\right){x}-1559a+659$ |
| 81225.1-a5 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.006926864$ |
$0.592251851$ |
2.754442525 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -76 a - 241\) , \( 591 a + 1422\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-76a-241\right){x}+591a+1422$ |
| 81225.3-a5 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.006926864$ |
$0.592251851$ |
2.754442525 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 241 a + 75\) , \( -592 a + 2014\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(241a+75\right){x}-592a+2014$ |
| 102675.1-a5 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.735094194$ |
5.123708641 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 35 a + 166\) , \( -1081 a + 831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(35a+166\right){x}-1081a+831$ |
| 102675.3-a5 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.735094194$ |
5.123708641 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 201 a - 166\) , \( 1081 a - 250\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(201a-166\right){x}+1081a-250$ |
*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.
