Elliptic curve isogeny class 16128.5-k over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-16128.5-k
• Conductor: 16128.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 16128.5-k over \(\Q(\sqrt{-7}) \)

Isogeny class 16128.5-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16128.5-k1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 48\) , \( -48\bigr] \)
16128.5-k2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12\) , \( 0\bigr] \)
16128.5-k3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 10\bigr] \)
16128.5-k4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -152\) , \( -672\bigr] \)

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