| 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 |
| 384.1-a1 |
384.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
384.1 |
\( 2^{7} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.37029$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.68193173$ |
1.059577155 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 44 a - 76\) , \( -224 a + 388\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(44a-76\right){x}-224a+388$ |
| 384.1-f1 |
384.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
384.1 |
\( 2^{7} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.37029$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.66634840$ |
1.828229915 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 44 a - 76\) , \( 224 a - 388\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(44a-76\right){x}+224a-388$ |
| 768.1-h1 |
768.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.595402747$ |
$12.66634840$ |
2.177066230 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 4\) , \( 4 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-4\right){x}+4a-8$ |
| 768.1-i1 |
768.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.68193173$ |
2.119154310 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 4\) , \( -4 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-4\right){x}-4a+8$ |
| 1152.1-c1 |
1152.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1152.1 |
\( 2^{7} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{7} \) |
$1.80340$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.479982109$ |
$10.08493725$ |
2.794715627 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 15\) , \( -13 a + 22\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10a-15\right){x}-13a+22$ |
| 1152.1-q1 |
1152.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1152.1 |
\( 2^{7} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{7} \) |
$1.80340$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.146673929$ |
1.774391923 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 15\) , \( 13 a - 22\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-15\right){x}+13a-22$ |
| 2304.1-s1 |
2304.1-s |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.308926134$ |
$10.08493725$ |
3.597470311 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 134 a - 231\) , \( -1031 a + 1786\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(134a-231\right){x}-1031a+1786$ |
| 2304.1-z1 |
2304.1-z |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{7} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.231723236$ |
$6.146673929$ |
3.289342713 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 134 a - 231\) , \( 1031 a - 1786\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(134a-231\right){x}+1031a-1786$ |
| 3072.1-k1 |
3072.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$24.70295035$ |
1.782781879 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 84 a - 143\) , \( -488 a + 846\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(84a-143\right){x}-488a+846$ |
| 3072.1-q1 |
3072.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$24.70295035$ |
1.782781879 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 10\) , \( -11 a + 19\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(6a-10\right){x}-11a+19$ |
| 3072.1-bp1 |
3072.1-bp |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.439823178$ |
$15.05621474$ |
3.128991203 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 84 a - 143\) , \( 488 a - 846\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(84a-143\right){x}+488a-846$ |
| 3072.1-bs1 |
3072.1-bs |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.994721194$ |
$15.05621474$ |
4.334883036 |
\( -\frac{4736}{3} a + 3840 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 6 a - 10\) , \( 11 a - 19\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(6a-10\right){x}+11a-19$ |
*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.
