Elliptic curve isogeny class 38.1-d over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-38.1-d
• Conductor: 38.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 38.1-d over \(\Q(\sqrt{19}) \)

Isogeny class 38.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
38.1-d1	\( \bigl[a\) , \( 1\) , \( a\) , \( -14\) , \( -51\bigr] \)
38.1-d2	\( \bigl[a\) , \( 1\) , \( a\) , \( -84\) , \( 2287\bigr] \)
38.1-d3	\( \bigl[a\) , \( 1\) , \( a\) , \( 11\) , \( -69\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph