Elliptic curve isogeny class 54.1-a over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-54.1-a
• Conductor: 54.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 54.1-a over \(\Q(\sqrt{19}) \)

Isogeny class 54.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
54.1-a1	\( \bigl[1\) , \( a\) , \( 1\) , \( 501 a - 2183\) , \( -13450 a + 58623\bigr] \)
54.1-a2	\( \bigl[1\) , \( a\) , \( 1\) , \( a + 2\) , \( 3\bigr] \)
54.1-a3	\( \bigl[1\) , \( a\) , \( 1\) , \( 31 a - 133\) , \( -242 a + 1055\bigr] \)
54.1-a4	\( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 23\) , \( -26 a + 109\bigr] \)