Elliptic curve isogeny class 4732.2-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4732.2-g
• Conductor: 4732.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 4732.2-g over \(\Q(\sqrt{-7}) \)

Isogeny class 4732.2-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
4732.2-g1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -15663\) , \( -755809\bigr] \)
4732.2-g2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -193\) , \( -1055\bigr] \)
4732.2-g3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 7\) , \( -7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph