Elliptic curve isogeny class 81.1-f over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-81.1-f
• Conductor: 81.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 81.1-f over \(\Q(\sqrt{19}) \)

Isogeny class 81.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
81.1-f1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 739 a + 3223\) , \( 3074 a + 13399\bigr] \)
81.1-f2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -26 a + 154\) , \( 14 a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph