Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-1458.1-f
Conductor 1458.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 1458.1-f over \(\Q(\sqrt{-1}) \)

Isogeny class 1458.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
1458.1-f1 \( \bigl[i\) , \( 1\) , \( 1\) , \( 31 i + 15\) , \( -2 i - 75\bigr] \)
1458.1-f2 \( \bigl[i\) , \( 1\) , \( 1\) , \( i\) , \( i\bigr] \)
1458.1-f3 \( \bigl[i\) , \( 1\) , \( 1\) , \( -14 i - 15\) , \( 27 i + 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph