Properties

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

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-d over \(\Q(\sqrt{-1}) \)

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

Curve label Weierstrass Coefficients
1458.1-d1 \( \bigl[i\) , \( 1\) , \( i\) , \( -28\) , \( 53\bigr] \)
1458.1-d2 \( \bigl[i\) , \( 1\) , \( i\) , \( -13\) , \( -29\bigr] \)
1458.1-d3 \( \bigl[i\) , \( 1\) , \( i\) , \( 2\) , \( 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph