Elliptic curve isogeny class 900.3-m over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-900.3-m
• Conductor: 900.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 900.3-m over \(\Q(\sqrt{6}) \)

Isogeny class 900.3-m contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
900.3-m1	\( \bigl[a\) , \( a\) , \( 0\) , \( -56 a - 138\) , \( 294 a + 720\bigr] \)
900.3-m2	\( \bigl[a\) , \( 0\) , \( a\) , \( -12 a + 27\) , \( 6 a - 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph