Elliptic curve isogeny class 4032.4-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4032.4-b
• Conductor: 4032.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 4032.4-b over \(\Q(\sqrt{-7}) \)

Isogeny class 4032.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4032.4-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
4032.4-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \)
4032.4-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \)
4032.4-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \)

Rank

Rank: \( 1 \)

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