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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-14175.1-b
• 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-b over \(\Q(\sqrt{-7}) \)

Isogeny class 14175.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
14175.1-b1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -1182\) , \( 16362\bigr] \)
14175.1-b2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -12\) , \( -18\bigr] \)
14175.1-b3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 78\) , \( 45\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph