Elliptic curve isogeny class 7.2-a over number field \(\Q(\sqrt{109}) \)

• Base field: \(\Q(\sqrt{109}) \)
• Label: 2.2.109.1-7.2-a
• Conductor: 7.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 7.2-a over \(\Q(\sqrt{109}) \)

Isogeny class 7.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.2-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -7 a - 31\) , \( -41 a - 197\bigr] \)
7.2-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -132 a - 621\) , \( -1842 a - 8698\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph