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

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-81.1-e
• 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-e over \(\Q(\sqrt{19}) \)

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

Curve label	Weierstrass Coefficients
81.1-e1	\( \bigl[1\) , \( -1\) , \( a\) , \( -36287 a - 158169\) , \( 4762730 a + 20760254\bigr] \)
81.1-e2	\( \bigl[1\) , \( -1\) , \( a\) , \( -250442 a - 1091649\) , \( -138942817 a - 605637703\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph