| 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 |
| 11025.3-a1 |
11025.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{3} \cdot 5^{2} \cdot 7^{8} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.034279949$ |
1.565989435 |
\( -\frac{81}{5} a + \frac{34074}{5} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 15 a\) , \( -4 a - 21\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+15a{x}-4a-21$ |
| 11025.3-a2 |
11025.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{9} \cdot 5^{6} \cdot 7^{8} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.678093316$ |
1.565989435 |
\( -\frac{190581}{125} a + \frac{1138323}{125} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -170 a + 100\) , \( 471 a - 732\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-170a+100\right){x}+471a-732$ |
| 11025.3-b1 |
11025.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{9} \cdot 5^{2} \cdot 7^{2} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$0.176556380$ |
$3.107413951$ |
2.534030791 |
\( -\frac{81}{5} a + \frac{34074}{5} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -8 a + 4\) , \( 3 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-8a+4\right){x}+3a-5$ |
| 11025.3-b2 |
11025.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{3} \cdot 5^{6} \cdot 7^{2} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.058852126$ |
$3.107413951$ |
2.534030791 |
\( -\frac{190581}{125} a + \frac{1138323}{125} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 5 a - 7\) , \( -9 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-7\right){x}-9a+9$ |
| 11025.3-c1 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{38} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.121967527$ |
2.253375518 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -988 a - 1651\) , \( 48169 a + 42560\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-988a-1651\right){x}+48169a+42560$ |
| 11025.3-c2 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.951480443$ |
2.253375518 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( -11 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}-11a-10$ |
| 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 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 317 a + 524\) , \( 3139 a + 2153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(317a+524\right){x}+3139a+2153$ |
| 11025.3-c4 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -88 a - 151\) , \( 169 a + 290\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-88a-151\right){x}+169a+290$ |
| 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 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -43 a - 76\) , \( -341 a - 217\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-76\right){x}-341a-217$ |
| 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 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1213 a - 2026\) , \( 33919 a + 30815\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1213a-2026\right){x}+33919a+30815$ |
| 11025.3-c7 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -718 a - 1201\) , \( -17891 a - 14032\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-718a-1201\right){x}-17891a-14032$ |
| 11025.3-c8 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.121967527$ |
2.253375518 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -19438 a - 32401\) , \( 2281669 a + 1971170\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19438a-32401\right){x}+2281669a+1971170$ |
*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.
