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
50.3-g1 50.3-g $1$
$1$
\(\Q(\sqrt{26}) \) $2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( - 2^{16} \cdot 5^{2} \)
$2.42325$
$(2,a), (5,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \)
$1$
$10.35008641$
2.029818946
\( -\frac{381845}{4} a - \frac{1902655}{4} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1110 a - 5658\) , \( -50480 a - 257398\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1110a-5658\right){x}-50480a-257398$
50.3-j1 50.3-j $1$
$1$
\(\Q(\sqrt{26}) \) $2$
$[2, 0]$
50.3
\( 2 \cdot 5^{2} \)
\( - 2^{4} \cdot 5^{2} \)
$2.42325$
$(2,a), (5,a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2^{2} \)
$0.705097487$
$10.35008641$
5.724880954
\( -\frac{381845}{4} a - \frac{1902655}{4} \)
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 2 a - 13\) , \( -4 a + 11\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a-13\right){x}-4a+11$
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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.
