Elliptic curve isogeny class 20000.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-20000.5-c
• Conductor: 20000.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 20000.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 20000.5-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20000.5-c1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a + 5\) , \( 7 a - 23\bigr] \)
20000.5-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 8 a - 11\) , \( -15 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph