Elliptic curve isogeny class 108.2-f over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-108.2-f
• Conductor: 108.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 108.2-f over \(\Q(\sqrt{19}) \)

Isogeny class 108.2-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
108.2-f1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( a - 4\) , \( -12\bigr] \)
108.2-f2	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -909 a + 3966\) , \( -13173 a + 57414\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph