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
1458.3-a1
1458.3-a
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2 \cdot 3^{9} \)
$1.56179$
$(a), (-a-1), (a-1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$0.359215854$
$5.368548284$
1.818176744
\( \frac{3915}{2} a + 4617 \)
\( \bigl[1\) , \( -1\) , \( a\) , \( a\) , \( -a\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+a{x}-a$
1458.3-a2
1458.3-a
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2^{3} \cdot 3^{19} \)
$1.56179$
$(a), (-a-1), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$0.119738618$
$1.789516094$
1.818176744
\( \frac{7983}{4} a + \frac{32823}{2} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 15\) , \( -27 a - 5\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a-15\right){x}-27a-5$
1458.3-b1
1458.3-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2^{5} \cdot 3^{19} \)
$1.56179$
$(a), (-a-1), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2^{2} \cdot 3 \cdot 5 \)
$0.022120226$
$1.760224345$
3.303876712
\( -\frac{211661}{216} a - \frac{136897}{108} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( a + 13\) , \( 28 a + 5\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+13\right){x}+28a+5$
1458.3-b2
1458.3-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2^{15} \cdot 3^{13} \)
$1.56179$
$(a), (-a-1), (a-1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \cdot 5 \)
$0.066360678$
$1.760224345$
3.303876712
\( \frac{278183}{768} a + \frac{396409}{384} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 10\) , \( -10 a - 3\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+10\right){x}-10a-3$
1458.3-c1
1458.3-c
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2 \cdot 3^{21} \)
$1.56179$
$(a), (-a-1), (a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \)
$1$
$1.789516094$
2.530757931
\( \frac{3915}{2} a + 4617 \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 2\) , \( 13 a + 15\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-2\right){x}+13a+15$
1458.3-c2
1458.3-c
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.3
\( 2 \cdot 3^{6} \)
\( 2^{3} \cdot 3^{7} \)
$1.56179$
$(a), (-a-1), (a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$5.368548284$
2.530757931
\( \frac{7983}{4} a + \frac{32823}{2} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a - 2\) , \( a + 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-2\right){x}+a+1$
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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.