Elliptic curve isogeny class 256.7-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-256.7-f
• Conductor: 256.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.7-f over \(\Q(\sqrt{57}) \)

Isogeny class 256.7-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
256.7-f1	\( \bigl[a\) , \( a\) , \( 0\) , \( 156 a + 511\) , \( 1124 a + 3681\bigr] \)
256.7-f2	\( \bigl[a\) , \( a\) , \( 0\) , \( 27845 a - 119009\) , \( 4907545 a - 20979323\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph