Elliptic curve isogeny class 200.1-f over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-200.1-f
• Conductor: 200.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 200.1-f over \(\Q(\sqrt{7}) \)

Isogeny class 200.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
200.1-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 1\) , \( -a + 1\bigr] \)
200.1-f2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 9\) , \( 3 a - 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph