Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-22500.13-e
Conductor 22500.13
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 22500.13-e over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.13-e contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
22500.13-e1 \( \bigl[1\) , \( -a\) , \( a\) , \( 58 a - 39\) , \( 194 a + 115\bigr] \)
22500.13-e2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -90 a + 87\) , \( -147 a + 721\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph