Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.1-c
Conductor 27225.1
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 27225.1-c over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
27225.1-c1 \( \bigl[0\) , \( -a\) , \( 1\) , \( -688189 a - 258072\) , \( -339338542 a + 201347357\bigr] \)
27225.1-c2 \( \bigl[0\) , \( -a\) , \( 1\) , \( -909 a - 342\) , \( -29132 a + 16667\bigr] \)
27225.1-c3 \( \bigl[0\) , \( -a\) , \( 1\) , \( -29 a - 12\) , \( 238 a - 163\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph