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

• Base field: \(\Q(\sqrt{109}) \)
• Label: 2.2.109.1-12.1-d
• 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-d over \(\Q(\sqrt{109}) \)

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

Curve label	Weierstrass Coefficients
12.1-d1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 527 a - 3015\) , \( 34652 a - 198215\bigr] \)
12.1-d2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 56647 a - 324030\) , \( 16772306 a - 95940161\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph