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
16.2-a1 16.2-a $4$
$4$
4.4.4913.1 $4$
$[4, 0]$
16.2
\( 2^{4} \)
\( - 2^{16} \)
$8.85782$
$(1/2a^3-a^2-2a+5/2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$502.9366260$
1.793824249
\( -78828400594 a^{3} + 40366354305 a^{2} + 492667383775 a + 161557746473 \)
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{15}{2} a^{3} - 8 a^{2} + 8 a + \frac{7}{2}\) , \( -\frac{61}{2} a^{3} - 53 a^{2} + 16 a + \frac{21}{2}\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{15}{2}a^{3}-8a^{2}+8a+\frac{7}{2}\right){x}-\frac{61}{2}a^{3}-53a^{2}+16a+\frac{21}{2}$
16.2-a2 16.2-a $4$
$4$
4.4.4913.1 $4$
$[4, 0]$
16.2
\( 2^{4} \)
\( 2^{8} \)
$8.85782$
$(1/2a^3-a^2-2a+5/2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 1 \)
$1$
$2011.746504$
1.793824249
\( -153101 a^{3} + 153101 a^{2} + 765505 a + 242916 \)
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 2 a^{2} + 8 a + \frac{7}{2}\) , \( -2 a^{3} + 2 a^{2} + 7 a + 2\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{5}{2}a^{3}+2a^{2}+8a+\frac{7}{2}\right){x}-2a^{3}+2a^{2}+7a+2$
16.2-a3 16.2-a $4$
$4$
4.4.4913.1 $4$
$[4, 0]$
16.2
\( 2^{4} \)
\( - 2^{16} \)
$8.85782$
$(1/2a^3-a^2-2a+5/2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$502.9366260$
1.793824249
\( -18765066078 a^{3} + 57227112367 a^{2} - 4700050415 a - 9151196745 \)
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} - 8 a^{2} + 13 a + \frac{7}{2}\) , \( \frac{11}{2} a^{3} + 22 a^{2} + 7 a - \frac{7}{2}\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-\frac{5}{2}a^{3}-8a^{2}+13a+\frac{7}{2}\right){x}+\frac{11}{2}a^{3}+22a^{2}+7a-\frac{7}{2}$
16.2-a4 16.2-a $4$
$4$
4.4.4913.1 $4$
$[4, 0]$
16.2
\( 2^{4} \)
\( 2^{16} \)
$8.85782$
$(1/2a^3-a^2-2a+5/2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$502.9366260$
1.793824249
\( -273 a^{3} + 273 a^{2} + 1365 a + 1124 \)
\( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a + \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{5}{2}\bigr] \) ${y}^2+\left(-\frac{1}{2}a^{3}+a^{2}+2a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-3a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{1}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}-3a+\frac{5}{2}\right){x}-\frac{1}{2}a^{3}+a^{2}+3a-\frac{5}{2}$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
