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 $2$
$5$
4.4.4913.1 $4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{70} \)
$7.44851$
$(1/2a^3-a^2-2a+5/2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.1.2 $25$
\( 1 \)
$1$
$2.545438365$
0.907881595
\( \frac{69419000739757}{34359738368} a^{3} - \frac{69419000739757}{34359738368} a^{2} - \frac{347095003698785}{34359738368} a - \frac{108360928343791}{34359738368} \)
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a\) , \( 18 a^{3} - 10 a^{2} - 107 a - 21\) , \( -\frac{251}{2} a^{3} + 210 a^{2} + 668 a - \frac{1203}{2}\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(18a^{3}-10a^{2}-107a-21\right){x}-\frac{251}{2}a^{3}+210a^{2}+668a-\frac{1203}{2}$
4.1-a2 4.1-a $2$
$5$
4.4.4913.1 $4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{14} \)
$7.44851$
$(1/2a^3-a^2-2a+5/2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.1.1 $1$
\( 1 \)
$1$
$1590.898978$
0.907881595
\( -\frac{346627}{128} a^{3} + \frac{346627}{128} a^{2} + \frac{1733135}{128} a - \frac{887903}{128} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}$
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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.
