Elliptic curve isogeny class 39204.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.4-a
• Conductor: 39204.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
39204.4-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a + 306\) , \( 1553 a - 822\bigr] \)
39204.4-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 57 a + 123\) , \( 1003 a - 1141\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph