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
5.1-a1
5.1-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
5.1
\( 5 \)
\( - 5^{9} \)
$3.16363$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$2.315249819$
$4.879543419$
1.251832761
\( -\frac{18942486647612346}{1953125} a^{2} + \frac{70018873198097803}{1953125} a - \frac{56200973797329704}{1953125} \)
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( a^{2} + a - 5\) , \( 188 a^{2} + 287 a - 596\) , \( -218 a^{2} - 330 a + 693\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(188a^{2}+287a-596\right){x}-218a^{2}-330a+693$
25.2-a2
25.2-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
25.2
\( 5^{2} \)
\( - 5^{15} \)
$4.13695$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.413768858$
$26.59709878$
2.438885047
\( -\frac{18942486647612346}{1953125} a^{2} + \frac{70018873198097803}{1953125} a - \frac{56200973797329704}{1953125} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -346 a^{2} - 48 a + 2317\) , \( -20185 a^{2} - 3650 a + 137192\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-346a^{2}-48a+2317\right){x}-20185a^{2}-3650a+137192$
80.3-b1
80.3-b
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
80.3
\( 2^{4} \cdot 5 \)
\( - 2^{12} \cdot 5^{9} \)
$5.02195$
$(a^2-6), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3^{2} \)
$0.182000073$
$20.19257700$
3.665009367
\( -\frac{18942486647612346}{1953125} a^{2} + \frac{70018873198097803}{1953125} a - \frac{56200973797329704}{1953125} \)
\( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} + a - 4\) , \( -a^{2} + 32 a - 37\) , \( 15 a^{2} - 85 a + 77\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{2}+32a-37\right){x}+15a^{2}-85a+77$
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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.