Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-30492.5-f
Conductor 30492.5
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 30492.5-f over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
30492.5-f1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
30492.5-f2 \( \bigl[1\) , \( 1\) , \( 0\) , \( -16\) , \( -20\bigr] \)
30492.5-f3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -126\) , \( 486\bigr] \)
30492.5-f4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -226\) , \( -1406\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph