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

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-18.1-a
• Conductor: 18.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
18.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -6112 a - 26627\) , \( -275601 a - 1201300\bigr] \)
18.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -46792 a - 203947\) , \( 11319975 a + 49342644\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph