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
248.1-b1 248.1-b $4$
$4$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
248.1
\( 2^{3} \cdot 31 \)
\( - 2^{11} \cdot 31 \)
$1.00299$
$(a), (-4a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 1 \)
$0.844058245$
$8.252359041$
1.231333066
\( -\frac{455569583015001}{31} a + \frac{644272682915546}{31} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 63 a + 59\) , \( -442 a - 566\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(63a+59\right){x}-442a-566$
496.1-a1 496.1-a $4$
$4$
\(\Q(\sqrt{2}) \) $2$
$[2, 0]$
496.1
\( 2^{4} \cdot 31 \)
\( - 2^{11} \cdot 31 \)
$1.19276$
$(a), (-4a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $4$
\( 2 \)
$1$
$2.260896180$
1.598695020
\( -\frac{455569583015001}{31} a + \frac{644272682915546}{31} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 61 a + 60\) , \( 504 a + 625\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(61a+60\right){x}+504a+625$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
