Elliptic curve isogeny class 124.1-c over number field \(\Q(\sqrt{93}) \)

• Base field: \(\Q(\sqrt{93}) \)
• Label: 2.2.93.1-124.1-c
• Conductor: 124.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 124.1-c over \(\Q(\sqrt{93}) \)

Isogeny class 124.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
124.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \)
124.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)
124.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \)
124.1-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph