Elliptic curve isogeny class 72.1-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-72.1-c
• Conductor: 72.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 72.1-c over \(\Q(\sqrt{6}) \)

Isogeny class 72.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
72.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a + 36\) , \( -52 a - 127\bigr] \)
72.1-c2	\( \bigl[a\) , \( -a\) , \( a\) , \( 23 a - 60\) , \( -70 a + 170\bigr] \)