Elliptic curve isogeny class 18.1-d over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-18.1-d
• Conductor: 18.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 18.1-d over \(\Q(\sqrt{19}) \)

Isogeny class 18.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
18.1-d1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 46789 a - 203942\) , \( 11366766 a - 49546594\bigr] \)
18.1-d2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 6109 a - 26622\) , \( -269490 a + 1174670\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph