Elliptic curve isogeny class 81.1-f over number field \(\Q(\sqrt{93}) \)

• Base field: \(\Q(\sqrt{93}) \)
• Label: 2.2.93.1-81.1-f
• Conductor: 81.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{93}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 23 \); class number \(1\).

Elliptic curves in class 81.1-f over \(\Q(\sqrt{93}) \)

Isogeny class 81.1-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
81.1-f1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 297 a - 1593\) , \( 6779 a - 36082\bigr] \)
81.1-f2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a - 78\) , \( -87 a - 376\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph