Elliptic curve isogeny class 432.2-f over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-432.2-f
• Conductor: 432.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 432.2-f over \(\Q(\sqrt{7}) \)

Isogeny class 432.2-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
432.2-f1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 9\) , \( 6 a - 19\bigr] \)
432.2-f2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -44 a - 112\) , \( 218 a + 575\bigr] \)