Elliptic curve isogeny class 5887.2-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-5887.2-e
• Conductor: 5887.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 5887.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 5887.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5887.2-e1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -9\) , \( 8\bigr] \)
5887.2-e2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a + 3\) , \( 3 a - 2\bigr] \)
5887.2-e3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a + 4\) , \( -4 a + 1\bigr] \)
5887.2-e4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -154\) , \( 675\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph