Elliptic curve isogeny class 4.2-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-4.2-a
• Conductor: 4.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 4.2-a over \(\Q(\sqrt{57}) \)

Isogeny class 4.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.2-a1	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 5\) , \( -a - 5\bigr] \)
4.2-a2	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 5\) , \( 17422 a - 74490\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph