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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.3-e
• Conductor: 144.3
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
144.3-e1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 13 a - 79\) , \( 113 a - 513\bigr] \)
144.3-e2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a - 4\) , \( 2 a - 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph