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-a2
5.1-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
5.1
\( 5 \)
\( - 5^{3} \)
$3.16363$
$(-a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$0.771749939$
$131.7476723$
1.251832761
\( -\frac{207221}{125} a^{2} - \frac{154322}{125} a + \frac{453296}{125} \)
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( a^{2} + a - 5\) , \( -32 a^{2} - 48 a + 104\) , \( 198 a^{2} + 301 a - 628\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-32a^{2}-48a+104\right){x}+198a^{2}+301a-628$
25.2-a1
25.2-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
25.2
\( 5^{2} \)
\( - 5^{9} \)
$4.13695$
$(-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.137922952$
$79.79129636$
2.438885047
\( -\frac{207221}{125} a^{2} - \frac{154322}{125} a + \frac{453296}{125} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 39 a^{2} + 7 a - 263\) , \( 802 a^{2} + 143 a - 5445\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(39a^{2}+7a-263\right){x}+802a^{2}+143a-5445$
80.3-b2
80.3-b
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
80.3
\( 2^{4} \cdot 5 \)
\( - 2^{12} \cdot 5^{3} \)
$5.02195$
$(a^2-6), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3 \)
$0.060666691$
$181.7331930$
3.665009367
\( -\frac{207221}{125} a^{2} - \frac{154322}{125} a + \frac{453296}{125} \)
\( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} + a - 4\) , \( -a^{2} - 3 a + 3\) , \( a^{2} + a - 3\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{2}-3a+3\right){x}+a^{2}+a-3$
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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.