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
86436.3-h2 86436.3-h $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
86436.3
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \)
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)
$2.65383$
$(-2a+1), (-3a+1), (3a-2), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B[2] $1$
\( 2 \cdot 3^{2} \)
$0.071245209$
$1.498465456$
4.437866884
\( \frac{189}{512} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( 39\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}+39$
15876.2-d2 15876.2-d $2$
$3$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
15876.2
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{18} \cdot 3^{18} \cdot 7^{4} \)
$2.65383$
$(a), (-a+1), (-2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.2 $1$
\( 2 \cdot 3 \)
$0.548686226$
$0.499488485$
2.486060889
\( \frac{189}{512} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( -1072\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}-1072$
882.1-b2 882.1-b $2$
$3$
\(\Q(\sqrt{-21}) \) $2$
$[0, 1]$
882.1
\( 2 \cdot 3^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 3^{18} \cdot 7^{4} \)
$4.46319$
$(2,a+1), (3,a), (7,a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B $4$
\( 2^{2} \)
$1$
$1.498465456$
5.231871529
\( \frac{189}{512} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( -1072\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2+12{x}-1072$
1764.1-b2 1764.1-b $2$
$3$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
1764.1
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)
$2.65383$
$(-a+2), (a+3), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2^{2} \cdot 3^{3} \)
$1$
$1.770823918$
4.637105514
\( \frac{189}{512} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -8 a + 21\) , \( 942 a - 2630\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+21\right){x}+942a-2630$
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Pari/GP
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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.
