Elliptic curve isogeny class 3872.15-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.15-b
• Conductor: 3872.15
• Rank: \( 1 \)

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

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

Elliptic curves in class 3872.15-b over \(\Q(\sqrt{-7}) \)

Isogeny class 3872.15-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3872.15-b1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -a + 8\) , \( -2 a\bigr] \)
3872.15-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -13 a\) , \( 20 a - 20\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph