Elliptic curve isogeny class 54.2-f over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-54.2-f
• Conductor: 54.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 54.2-f over \(\Q(\sqrt{19}) \)

Isogeny class 54.2-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
54.2-f1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 270344 a + 1178405\) , \( 385746767 a + 1681431175\bigr] \)
54.2-f2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 49819 a - 217146\) , \( 10523888 a - 45872558\bigr] \)