Elliptic curve isogeny class 242.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-242.1-a
• Conductor: 242.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 242.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 242.1-a contains 4 curves linked by isogenies of degrees dividing 22.

Curve label	Weierstrass Coefficients
242.1-a1	\( \bigl[1\) , \( 1\) , \( a\) , \( 35 a - 135\) , \( -217 a + 705\bigr] \)
242.1-a2	\( \bigl[1\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
242.1-a3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a - 1\) , \( -1\bigr] \)
242.1-a4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 404 a - 86\) , \( 1731 a + 3810\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 11 & 22 & 2 \\ 11 & 1 & 2 & 22 \\ 22 & 2 & 1 & 11 \\ 2 & 22 & 11 & 1 \end{array}\right)\)

Isogeny graph