Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{229}) \)

• Base field: \(\Q(\sqrt{229}) \)
• Label: 2.2.229.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{229}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 57 \); class number \(3\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{229}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a\) , \( 0\) , \( a\) , \( 22 a - 285\) , \( 307 a - 3606\bigr] \)
1.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 3\) , \( 2 a + 6\bigr] \)
1.1-a3	\( \bigl[a\) , \( 0\) , \( a\) , \( -3 a\) , \( -3 a + 9\bigr] \)
1.1-a4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -24 a - 263\) , \( -308 a - 3299\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph