Elliptic curve isogeny class 12.1-a over number field \(\Q(\sqrt{109}) \)

• Base field: \(\Q(\sqrt{109}) \)
• Label: 2.2.109.1-12.1-a
• Conductor: 12.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{109}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 27 \); class number \(1\).

Elliptic curves in class 12.1-a over \(\Q(\sqrt{109}) \)

Isogeny class 12.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
12.1-a1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2926 a + 16736\) , \( 111936 a - 640300\bigr] \)
12.1-a2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 379 a - 2164\) , \( -10536 a + 60269\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph