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
4.1-a1
4.1-a
$2$
$5$
4.4.18097.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( - 2^{10} \)
$14.29550$
$(a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 5 \)
$1.494323611$
$13.87623719$
3.082783857
\( \frac{53826719946875}{64} a^{3} - \frac{185108694165561}{64} a^{2} + \frac{87531672190689}{64} a + \frac{20537254296311}{16} \)
\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - 14 a - 48\) , \( 38 a^{3} - 31 a^{2} - 170 a - 4\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{3}-a^{2}-14a-48\right){x}+38a^{3}-31a^{2}-170a-4$
4.1-a2
4.1-a
$2$
$5$
4.4.18097.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( - 2^{2} \)
$14.29550$
$(a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$0.298864722$
$346.9059298$
3.082783857
\( \frac{25621}{4} a^{3} + \frac{38575}{4} a^{2} - \frac{77051}{4} a - \frac{16681}{2} \)
\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - 9 a - 3\) , \( 4 a^{3} + 8 a^{2} - 15 a - 7\bigr] \)
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{3}+4a^{2}-9a-3\right){x}+4a^{3}+8a^{2}-15a-7$
4.1-b1
4.1-b
$2$
$5$
4.4.18097.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( - 2^{10} \)
$14.29550$
$(a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$25$
\( 1 \)
$1$
$1.030730532$
0.191549867
\( \frac{53826719946875}{64} a^{3} - \frac{185108694165561}{64} a^{2} + \frac{87531672190689}{64} a + \frac{20537254296311}{16} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1131}{2} a^{3} + \frac{1881}{2} a^{2} + \frac{7159}{2} a - 5779\) , \( -\frac{39037}{2} a^{3} + \frac{58751}{2} a^{2} + \frac{247527}{2} a - 179770\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}^{2}+\left(-\frac{1131}{2}a^{3}+\frac{1881}{2}a^{2}+\frac{7159}{2}a-5779\right){x}-\frac{39037}{2}a^{3}+\frac{58751}{2}a^{2}+\frac{247527}{2}a-179770$
4.1-b2
4.1-b
$2$
$5$
4.4.18097.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( - 2^{2} \)
$14.29550$
$(a)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$644.2065829$
0.191549867
\( \frac{25621}{4} a^{3} + \frac{38575}{4} a^{2} - \frac{77051}{4} a - \frac{16681}{2} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 4 a\) , \( -2 a^{2} + 5\) , \( \frac{11}{2} a^{3} - \frac{5}{2} a^{2} - \frac{61}{2} a - 12\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}+5\right){x}+\frac{11}{2}a^{3}-\frac{5}{2}a^{2}-\frac{61}{2}a-12$
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*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.