Elliptic curve isogeny class 36.1-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-36.1-f
• Conductor: 36.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.1-f over \(\Q(\sqrt{57}) \)

Isogeny class 36.1-f contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
36.1-f1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5675 a - 23939\) , \( 560829 a + 1687167\bigr] \)
36.1-f2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -64690451 a - 211855871\) , \( 550295059293 a + 1802170764457\bigr] \)
36.1-f3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 1\) , \( 3 a + 27\bigr] \)
36.1-f4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 193879 a + 634939\) , \( -82120563 a - 268938047\bigr] \)

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