Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-19404.2-e
Conductor 19404.2
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 19404.2-e over \(\Q(\sqrt{-11}) \)

Isogeny class 19404.2-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
19404.2-e1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -405\) , \( 4731\bigr] \)
19404.2-e2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -7445\) , \( 244091\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph