Elliptic curve isogeny class 39204.5-k over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.5-k
• Conductor: 39204.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.5-k over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.5-k contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
39204.5-k1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -365\) , \( 15005\bigr] \)
39204.5-k2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( -547\bigr] \)
39204.5-k3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -50\) , \( -115\bigr] \)
39204.5-k4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -725\) , \( 7661\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph