Elliptic curve isogeny class 4356.6-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.6-a
• Conductor: 4356.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.6-a over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.6-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4356.6-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -8 a + 4\) , \( 2 a - 34\bigr] \)
4356.6-a2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -12 a + 27\) , \( -17 a - 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph