Elliptic curve isogeny class 100.1-l over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-100.1-l
• Conductor: 100.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{23}) \)

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

Elliptic curves in class 100.1-l over \(\Q(\sqrt{23}) \)

Isogeny class 100.1-l contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-l1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2182 a - 10441\) , \( 186753 a - 895614\bigr] \)
100.1-l2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -218 a + 1069\) , \( -4207 a + 20198\bigr] \)
100.1-l3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-l4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph