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
161.2-a1 161.2-a $3$
$9$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
161.2
\( 7 \cdot 23 \)
\( 7 \cdot 23 \)
$0.84216$
$(-2a+1), (2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 1 \)
$1$
$8.674582374$
0.728596434
\( -\frac{262144}{161} a - \frac{98304}{161} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a - 1\) , \( -1\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-1\right){x}-1$
161.2-a2 161.2-a $3$
$9$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
161.2
\( 7 \cdot 23 \)
\( 7 \cdot 23^{9} \)
$0.84216$
$(-2a+1), (2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $1$
\( 1 \)
$1$
$0.963842486$
0.728596434
\( -\frac{72000442968309760}{12608068630241} a + \frac{291812157579067392}{12608068630241} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 61 a + 9\) , \( 62 a + 261\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(61a+9\right){x}+62a+261$
161.2-a3 161.2-a $3$
$9$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
161.2
\( 7 \cdot 23 \)
\( 7^{3} \cdot 23^{3} \)
$0.84216$
$(-2a+1), (2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs.1.1 $1$
\( 3 \)
$1$
$2.891527458$
0.728596434
\( \frac{27960770560}{596183} a + \frac{64831717376}{596183} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 11 a - 1\) , \( 2 a - 24\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a-1\right){x}+2a-24$
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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.
