Elliptic curve isogeny class 200.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-200.1-a
• Conductor: 200.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 200.1-a over \(\Q(\sqrt{11}) \)

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

Curve label	Weierstrass Coefficients
200.1-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 197 a + 652\) , \( 5608 a + 18598\bigr] \)
200.1-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -103 a - 343\) , \( 621 a + 2058\bigr] \)
200.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
200.1-a4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -1603 a - 5318\) , \( 59476 a + 197258\bigr] \)

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