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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.5-c
• 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-c over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
39204.5-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -147\) , \( -135\bigr] \)
39204.5-c2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -582\) , \( -5068\bigr] \)
39204.5-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -87\) , \( 333\bigr] \)
39204.5-c4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -9222\) , \( -338572\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph