Elliptic curve isogeny class 256.6-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-256.6-c
• Conductor: 256.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.6-c over \(\Q(\sqrt{57}) \)

Isogeny class 256.6-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
256.6-c1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 4 a + 11\) , \( 5 a + 15\bigr] \)
256.6-c2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -11 a - 39\) , \( 11 a + 35\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph