Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-29241.3-c
Conductor 29241.3
Rank \( 1 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 29241.3-c over \(\Q(\sqrt{-11}) \)

Isogeny class 29241.3-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
29241.3-c1 \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -7 a - 12\) , \( 224 a + 190\bigr] \)
29241.3-c2 \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -22 a - 42\) , \( 113 a + 76\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph