Properties

Base field \(\Q(\sqrt{11}) \)
Label 2.2.44.1-25.1-b
Conductor 25.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 25.1-b over \(\Q(\sqrt{11}) \)

Isogeny class 25.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
25.1-b1 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4 a - 5\) , \( -a\bigr] \)
25.1-b2 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 128 a - 420\) , \( 1486 a - 4926\bigr] \)
25.1-b3 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 3 a - 5\) , \( a\bigr] \)
25.1-b4 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -129 a - 420\) , \( -1486 a - 4926\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph