Elliptic curve isogeny class 8064.2-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-8064.2-e
• Conductor: 8064.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 8064.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 8064.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
8064.2-e1	\( \bigl[a\) , \( -a\) , \( a\) , \( 156 a - 371\) , \( 1601 a - 2234\bigr] \)
8064.2-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 59 a + 13\) , \( -23 a - 335\bigr] \)
8064.2-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 59 a - 147\) , \( 617 a - 1391\bigr] \)
8064.2-e4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -38 a + 40\) , \( -76 a + 168\bigr] \)

Rank

Rank: \( 1 \)

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