Elliptic curve isogeny class 256.1-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-256.1-b
• Conductor: 256.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 256.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 256.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
256.1-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 44320 a - 189464\) , \( 9682784 a - 41393100\bigr] \)
256.1-b2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 10\) , \( 204 a - 884\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph