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

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

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

Curve label	Weierstrass Coefficients
39204.5-e1	\( \bigl[1\) , \( -1\) , \( a\) , \( 706 a + 6\) , \( -8063 a + 25854\bigr] \)
39204.5-e2	\( \bigl[1\) , \( -1\) , \( a\) , \( -374 a + 366\) , \( -359 a + 4470\bigr] \)
39204.5-e3	\( \bigl[1\) , \( -1\) , \( a\) , \( 3811 a + 1716\) , \( -23093 a + 190014\bigr] \)
39204.5-e4	\( \bigl[1\) , \( -1\) , \( a\) , \( 60241 a + 27546\) , \( -1393811 a + 12416424\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph