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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.4-g
• 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-g over \(\Q(\sqrt{57}) \)

Isogeny class 144.4-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.4-g1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3\) , \( 636 a + 2082\bigr] \)
144.4-g2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -7286 a + 31183\) , \( -910322 a + 3891612\bigr] \)
144.4-g3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 23 a - 64\) , \( -62 a + 320\bigr] \)
144.4-g4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 98 a - 409\) , \( 916 a - 3910\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph