Elliptic curve isogeny class 224.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-224.1-a
• Conductor: 224.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 224.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 224.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
224.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
224.1-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -2 a + 1\) , \( 1\bigr] \)
224.1-a3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -7 a + 1\) , \( -6 a + 11\bigr] \)
224.1-a4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -12 a + 6\) , \( 14 a - 13\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph