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
3.1-a2
3.1-a
$6$
$8$
4.4.10273.1
$4$
$[4, 0]$
3.1
\( 3 \)
\( - 3^{4} \)
$10.39028$
$(-a^2+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$392.2876592$
0.483800168
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \)
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 4 a^{3} - 5 a^{2} - 25 a - 12\) , \( -10 a^{3} + 14 a^{2} + 57 a + 26\bigr] \)
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(4a^{3}-5a^{2}-25a-12\right){x}-10a^{3}+14a^{2}+57a+26$
9.1-a3
9.1-a
$6$
$8$
4.4.10273.1
$4$
$[4, 0]$
9.1
\( 3^{2} \)
\( - 3^{10} \)
$11.91976$
$(-a^2+1)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
\( 2^{2} \)
$1$
$312.1706310$
1.657952696
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \)
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 3\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( 0\) , \( -2 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{3} + 5 a^{2} - 3 a - 4\bigr] \)
${y}^2+\left(2a^{3}-5a^{2}-5a+3\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a\right){x}^{2}+\left(-2a^{3}+7a^{2}+2a-1\right){x}-a^{3}+5a^{2}-3a-4$
48.2-b4
48.2-b
$6$
$8$
4.4.10273.1
$4$
$[4, 0]$
48.2
\( 2^{4} \cdot 3 \)
\( - 2^{12} \cdot 3^{4} \)
$14.69408$
$(a), (-a^2+1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.263991273$
$1003.287237$
2.613161283
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \)
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 4\) , \( a^{3} - 2 a^{2} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 4 a^{3} - 9 a^{2} - 14 a + 8\) , \( 3 a^{3} - 8 a^{2} - 8 a + 12\bigr] \)
${y}^2+\left(2a^{3}-5a^{2}-6a+4\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a-1\right){x}^{2}+\left(4a^{3}-9a^{2}-14a+8\right){x}+3a^{3}-8a^{2}-8a+12$
144.2-a2
144.2-a
$6$
$8$
4.4.10273.1
$4$
$[4, 0]$
144.2
\( 2^{4} \cdot 3^{2} \)
\( - 2^{12} \cdot 3^{10} \)
$16.85709$
$(a), (-a^2+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$144.3014135$
2.847422661
\( -\frac{490913}{81} a^{3} + \frac{614549}{81} a^{2} + \frac{986851}{27} a + \frac{1612993}{81} \)
\( \bigl[a^{3} - 2 a^{2} - 3 a\) , \( -1\) , \( a\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( a - 1\bigr] \)
${y}^2+\left(a^{3}-2a^{2}-3a\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a^{3}-3a^{2}-2a+3\right){x}+a-1$
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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.