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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-256.1-a
• Conductor: 256.1
• Rank: \( 0 \)

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

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

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

Isogeny class 256.1-a contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
256.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10282063 a - 33672998\) , \( 34886965210 a + 114251923320\bigr] \)
256.1-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10282065 a - 43955062\) , \( -34876683146 a + 149094933468\bigr] \)
256.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3823 a - 12518\) , \( 369018 a + 1208504\bigr] \)
256.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3825 a - 16342\) , \( -365194 a + 1561180\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph