Elliptic curve isogeny class 144.2-k over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.2-k
• Conductor: 144.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 144.2-k over \(\Q(\sqrt{57}) \)

Isogeny class 144.2-k contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
144.2-k1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 171 a - 744\) , \( 1383 a - 5919\bigr] \)
144.2-k2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -103642 a + 443048\) , \( 20181596 a - 86274659\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph