Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-9216.7-c
Conductor 9216.7
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 9216.7-c over \(\Q(\sqrt{-7}) \)

Isogeny class 9216.7-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
9216.7-c1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 3 a + 14\) , \( -3 a - 14\bigr] \)
9216.7-c2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a + 8\) , \( 0\bigr] \)
9216.7-c3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 3 a + 174\) , \( -675 a + 306\bigr] \)
9216.7-c4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a + 40\) , \( -4 a - 148\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph