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
392.1-a1
392.1-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{2} \)
$0.79523$
$(a+1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.059979974$
$6.395739286$
0.767232560
\( -\frac{4}{7} \)
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i\) , \( 0\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}-i{x}$
392.1-a2
392.1-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{4} \)
$0.79523$
$(a+1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.119959949$
$3.197869643$
0.767232560
\( \frac{3543122}{49} \)
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 10\) , \( 10 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+10\right){x}+10i$
392.1-b1
392.1-b
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{2} \)
$0.79523$
$(a+1), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$8.032591436$
1.004073929
\( \frac{432}{7} \)
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i-1\right){x}-i$
392.1-b2
392.1-b
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{8} \)
$0.79523$
$(a+1), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$2.008147859$
1.004073929
\( \frac{11090466}{2401} \)
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 14\) , \( 24 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+14\right){x}+24i$
392.1-b3
392.1-b
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{4} \)
$0.79523$
$(a+1), (7)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$4.016295718$
1.004073929
\( \frac{740772}{49} \)
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 4\) , \( -2 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+4\right){x}-2i$
392.1-b4
392.1-b
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{2} \)
$0.79523$
$(a+1), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$2.008147859$
1.004073929
\( \frac{1443468546}{7} \)
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 74\) , \( -212 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+74\right){x}-212i$
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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.