Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-40.1-b
Conductor 40.1
Rank not recorded

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Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 40.1-b over \(\Q(\sqrt{10}) \)

Isogeny class 40.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
40.1-b1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \)
40.1-b2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \)
40.1-b3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
40.1-b4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph