Elliptic curve isogeny class 9.2-a over number field \(\Q(\sqrt{229}) \)

• Base field: \(\Q(\sqrt{229}) \)
• Label: 2.2.229.1-9.2-a
• Conductor: 9.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 9.2-a over \(\Q(\sqrt{229}) \)

Isogeny class 9.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 755121 a - 6091088\) , \( 982309525 a - 7923675006\bigr] \)
9.2-a2	\( \bigl[a\) , \( a\) , \( a\) , \( 23 a - 21\) , \( -a + 523\bigr] \)
9.2-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 9336 a - 75308\) , \( 1341295 a - 10819386\bigr] \)
9.2-a4	\( \bigl[a\) , \( a\) , \( a\) , \( 33 a - 126\) , \( 144 a - 797\bigr] \)

Rank

Rank: \( 1 \)

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