Elliptic curve isogeny class 200.1-a over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-200.1-a
• Conductor: 200.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 200.1-a over \(\Q(\sqrt{23}) \)

Isogeny class 200.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-a1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 786 a + 3770\) , \( 52378 a + 251196\bigr] \)
200.1-a2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -414 a - 1985\) , \( 6798 a + 32602\bigr] \)
200.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
200.1-a4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -6414 a - 30760\) , \( 584948 a + 2805312\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph