| 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-a3 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.322695746 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 1875.1-b3 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{28} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.223570171$ |
1.032626388 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+874{x}-5227$ |
| 11025.1-c3 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 5^{16} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.243935055$ |
2.253375518 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -525 a - 315\) , \( -2299 a + 4767\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-525a-315\right){x}-2299a+4767$ |
| 11025.3-c3 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 5^{16} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.243935055$ |
2.253375518 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 317 a + 524\) , \( 3139 a + 2153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(317a+524\right){x}+3139a+2153$ |
| 12675.1-a3 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.310036044$ |
2.863990301 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 281 a - 525\) , \( -1491 a - 1033\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(281a-525\right){x}-1491a-1033$ |
| 12675.3-a3 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.310036044$ |
2.863990301 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 525 a - 279\) , \( 1246 a - 1999\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(525a-279\right){x}+1246a-1999$ |
| 19200.1-g3 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{16} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.650156421$ |
$0.279462714$ |
3.356843389 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 560\) , \( 2900\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+560{x}+2900$ |
| 57600.1-j3 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{16} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1680 a\) , \( -17400 a + 8700\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+1680a{x}-17400a+8700$ |
| 57600.1-k3 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{10} \cdot 5^{16} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.329321481$ |
$0.161347873$ |
3.971591054 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1678 a + 1679\) , \( 15721 a - 7021\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1678a+1679\right){x}+15721a-7021$ |
| 81225.1-a3 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{10} \cdot 5^{16} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.027707458$ |
$0.148062962$ |
2.754442525 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 524 a + 1679\) , \( -6249 a - 13968\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(524a+1679\right){x}-6249a-13968$ |
| 81225.3-a3 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{10} \cdot 5^{16} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.027707458$ |
$0.148062962$ |
2.754442525 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -1679 a - 525\) , \( 6248 a - 20216\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-1679a-525\right){x}+6248a-20216$ |
| 102675.1-a3 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.183773548$ |
5.123708641 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -245 a - 1154\) , \( 10719 a - 8079\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-245a-1154\right){x}+10719a-8079$ |
| 102675.3-a3 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.183773548$ |
5.123708641 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1399 a + 1154\) , \( -10719 a + 2640\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-1399a+1154\right){x}-10719a+2640$ |
*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.
