Elliptic curve isogeny class 144.4-d over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.4-d
• Conductor: 144.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.4-d over \(\Q(\sqrt{57}) \)

Isogeny class 144.4-d contains 2 curves linked by isogenies of degree 19.

Curve label	Weierstrass Coefficients
144.4-d1	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -2226 a - 7290\) , \( 111180 a + 364104\bigr] \)
144.4-d2	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 414 a - 1770\) , \( -8919 a + 38121\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph