Elliptic curve isogeny class 4356.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.4-a
• Conductor: 4356.4
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 4356.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4356.4-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 8 a - 4\) , \( -2 a - 32\bigr] \)
4356.4-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 11 a + 16\) , \( 16 a - 40\bigr] \)