| 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 |
| 78400.2-a1 |
78400.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{10} \cdot 7^{6} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
$0.011277526$ |
$0.457060343$ |
2.142689697 |
\( -\frac{30211716096}{1071875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -412\) , \( 3316\bigr] \) |
${y}^2={x}^{3}-412{x}+3316$ |
| 78400.2-b1 |
78400.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{8} \cdot 7^{4} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.691494724$ |
1.596938661 |
\( \frac{10678754}{30625} a + \frac{30044446}{30625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a + 58\) , \( 41 a + 201\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a+58\right){x}+41a+201$ |
| 78400.2-b2 |
78400.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{2} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.382989449$ |
1.596938661 |
\( -\frac{24375452}{175} a + 17568 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 58\) , \( 185 a - 111\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a+58\right){x}+185a-111$ |
| 78400.2-c1 |
78400.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{2} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.382989449$ |
1.596938661 |
\( \frac{24375452}{175} a - \frac{21301052}{175} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 61 a - 58\) , \( -185 a + 74\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(61a-58\right){x}-185a+74$ |
| 78400.2-c2 |
78400.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{8} \cdot 7^{4} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.691494724$ |
1.596938661 |
\( -\frac{10678754}{30625} a + \frac{232704}{175} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 101 a - 58\) , \( -41 a + 242\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(101a-58\right){x}-41a+242$ |
| 78400.2-d1 |
78400.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{2} \cdot 7^{2} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.097431715$ |
$3.073025053$ |
2.765832067 |
\( -\frac{1024}{35} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 5\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}+5$ |
| 78400.2-e1 |
78400.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{4} \cdot 7^{12} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.278521437$ |
3.216088539 |
\( \frac{5265266308346}{1412376245} a - \frac{159677937425154}{7061881225} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -128 a - 976\) , \( -2944 a - 12020\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-128a-976\right){x}-2944a-12020$ |
| 78400.2-e2 |
78400.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{8} \cdot 7^{6} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.557042875$ |
3.216088539 |
\( \frac{1920508084}{2100875} a - \frac{7387021088}{10504375} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -128 a + 24\) , \( 656 a - 820\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-128a+24\right){x}+656a-820$ |
| 78400.2-f1 |
78400.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{4} \cdot 7^{12} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.278521437$ |
3.216088539 |
\( -\frac{5265266308346}{1412376245} a - \frac{133351605883424}{7061881225} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1104 a + 976\) , \( 2944 a - 14964\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1104a+976\right){x}+2944a-14964$ |
| 78400.2-f2 |
78400.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.2 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{8} \cdot 7^{6} \) |
$2.58987$ |
$(-3a+1), (3a-2), (2), (5)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.557042875$ |
3.216088539 |
\( -\frac{1920508084}{2100875} a + \frac{2215519332}{10504375} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -104 a - 24\) , \( -656 a - 164\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-104a-24\right){x}-656a-164$ |
*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.
