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
5.2-a1 5.2-a $1$
$1$
4.4.16997.1 $4$
$[4, 0]$
5.2
\( 5 \)
\( 5^{2} \)
$14.24610$
$(-a^2-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$0.036411483$
$1317.379880$
2.943426863
\( \frac{8133357}{25} a^{3} + \frac{7223444}{25} a^{2} - \frac{42380619}{25} a - \frac{9156051}{5} \)
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 3 a + 1\) , \( a + 1\) , \( -a^{3} + 2 a\) , \( -a\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-a^{3}+2a\right){x}-a$
5.2-b1 5.2-b $2$
$5$
4.4.16997.1 $4$
$[4, 0]$
5.2
\( 5 \)
\( 5^{10} \)
$14.24610$
$(-a^2-a+1)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.1.1 $1$
\( 2 \cdot 5 \)
$2.708762032$
$86.84611140$
2.887055124
\( \frac{3364042267}{9765625} a^{3} + \frac{1964925889}{9765625} a^{2} - \frac{25655280414}{9765625} a - \frac{3815938726}{1953125} \)
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -5 a^{3} - 12 a^{2} + a + 10\) , \( -30 a^{3} - 71 a^{2} + 13 a + 63\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a^{3}-12a^{2}+a+10\right){x}-30a^{3}-71a^{2}+13a+63$
5.2-b2 5.2-b $2$
$5$
4.4.16997.1 $4$
$[4, 0]$
5.2
\( 5 \)
\( 5^{2} \)
$14.24610$
$(-a^2-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.1.2 $25$
\( 2 \)
$13.54381016$
$0.138953778$
2.887055124
\( \frac{5357496973442499987}{25} a^{3} + \frac{4190018497495156254}{25} a^{2} - \frac{29759807723130703029}{25} a - \frac{6303903372448402516}{5} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 3\) , \( a\) , \( -1147 a^{3} + 1237 a^{2} + 5259 a - 4929\) , \( -37920 a^{3} + 42325 a^{2} + 176448 a - 163829\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-1147a^{3}+1237a^{2}+5259a-4929\right){x}-37920a^{3}+42325a^{2}+176448a-163829$
Download
displayed columns for
to
Text
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.
