Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-22500.8-i
Conductor 22500.8
Rank \( 0 \)

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 22500.8-i over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.8-i contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
22500.8-i1 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 9 a - 3\) , \( 12 a + 21\bigr] \)
22500.8-i2 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 84 a - 28\) , \( -1088 a - 1904\bigr] \)
22500.8-i3 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2484 a - 828\) , \( -36288 a - 63504\bigr] \)
22500.8-i4 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 159 a - 53\) , \( 612 a + 1071\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph