Elliptic curve isogeny class 11.1-c over number field \(\Q(\sqrt{165}) \)

• Base field: \(\Q(\sqrt{165}) \)
• Label: 2.2.165.1-11.1-c
• Conductor: 11.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{165}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).

Elliptic curves in class 11.1-c over \(\Q(\sqrt{165}) \)

Isogeny class 11.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
11.1-c1	\( \bigl[0\) , \( a\) , \( 1\) , \( -101664 a - 602152\) , \( 44484722 a + 263466147\bigr] \)
11.1-c2	\( \bigl[0\) , \( a\) , \( 1\) , \( -134 a - 782\) , \( 3582 a + 21207\bigr] \)
11.1-c3	\( \bigl[0\) , \( a\) , \( 1\) , \( -4 a - 12\) , \( -38 a - 233\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph