Elliptic curve isogeny class 14175.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-14175.1-a
• Conductor: 14175.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 14175.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 14175.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14175.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 157\) , \( 992\bigr] \)
14175.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -68\) , \( 182\bigr] \)
14175.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -23\) , \( -34\bigr] \)
14175.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1013\) , \( 12656\bigr] \)

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