Elliptic curve isogeny class 625.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-625.1-f
• Conductor: 625.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 625.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 625.1-f contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
625.1-f1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -59 a + 144\) , \( 1183 a - 2897\bigr] \)
625.1-f2	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 209 a - 506\) , \( 2454 a - 6011\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph