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

• Base field: \(\Q(\sqrt{93}) \)
• Label: 2.2.93.1-81.1-d
• 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-d over \(\Q(\sqrt{93}) \)

Isogeny class 81.1-d contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
81.1-d1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -29 a - 122\) , \( 259 a + 1120\bigr] \)
81.1-d2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 31 a - 152\) , \( -229 a + 1227\bigr] \)
81.1-d3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 21 a - 112\bigr] \)
81.1-d4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -21 a - 91\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph