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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-16128.5-e
• Conductor: 16128.5
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
16128.5-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -52\bigr] \)
16128.5-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -392\) , \( 228\bigr] \)
16128.5-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -252\) , \( -1620\bigr] \)
16128.5-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4032\) , \( -99900\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph