Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-2500.2-a
Conductor 2500.2
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 2500.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 2500.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
2500.2-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
2500.2-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
2500.2-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
2500.2-a4 \( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph