Properties

Base field \(\Q(\sqrt{41}) \)
Label 2.2.41.1-256.4-a
Conductor 256.4
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{41}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 10 \); class number \(1\).

Elliptic curves in class 256.4-a over \(\Q(\sqrt{41}) \)

Isogeny class 256.4-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
256.4-a1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 414 a + 1123\) , \( -8297 a - 22413\bigr] \)
256.4-a2 \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 14\) , \( 2 a - 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph