Elliptic curve isogeny class 144.3-k over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.3-k
• Conductor: 144.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.3-k over \(\Q(\sqrt{57}) \)

Isogeny class 144.3-k contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
144.3-k1	\( \bigl[a\) , \( -1\) , \( a\) , \( 103640 a + 339408\) , \( -20181597 a - 66093062\bigr] \)
144.3-k2	\( \bigl[a\) , \( -1\) , \( a\) , \( -173 a - 571\) , \( -1384 a - 4535\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph