Elliptic curve isogeny class 42592.18-j over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-42592.18-j
• Conductor: 42592.18
• Rank: \( 1 \)

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

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

Elliptic curves in class 42592.18-j over \(\Q(\sqrt{-7}) \)

Isogeny class 42592.18-j contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
42592.18-j1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -69 a + 58\) , \( -102 a + 470\bigr] \)
42592.18-j2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( a + 8\) , \( -4 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph