Elliptic curve isogeny class 9072.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9072.1-a
• Conductor: 9072.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 9072.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 9072.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9072.1-a1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -138 a - 99\) , \( 1214 a - 68\bigr] \)
9072.1-a2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 33 a + 3\) , \( -41 a - 98\bigr] \)
9072.1-a3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -3 a - 9\) , \( 35 a - 14\bigr] \)
9072.1-a4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 24 a - 6\) , \( 4 a + 59\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph