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-d3 392.1-d $6$
$8$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{6} \)
$1.12462$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$1$
$14.53019657$
1.284300066
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a - 7\) , \( 7 a + 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a-7\right){x}+7a+9$
784.1-b3 784.1-b $6$
$8$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{6} \)
$1.33740$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{2} \)
$1$
$16.66110717$
1.472647733
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a - 7\) , \( -7 a - 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-7\right){x}-7a-9$
2744.1-b3 2744.1-b $6$
$8$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
2744.1
\( 2^{3} \cdot 7^{3} \)
\( 2^{4} \cdot 7^{12} \)
$1.82928$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$1$
$4.405166484$
1.557461546
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 43 a - 68\) , \( 225 a - 323\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(43a-68\right){x}+225a-323$
2744.2-j3 2744.2-j $6$
$8$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
2744.2
\( 2^{3} \cdot 7^{3} \)
\( 2^{4} \cdot 7^{12} \)
$1.82928$
$(a), (-2a+1), (2a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cs $1$
\( 2^{4} \)
$0.500955107$
$7.850819298$
2.780985937
\( -\frac{4566144}{2401} a + \frac{14497232}{2401} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -12 a - 31\) , \( 28 a + 48\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-31\right){x}+28a+48$
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Pari/GP
SageMath
Magma
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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.
