Elliptic curve isogeny class 54.1-b over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-54.1-b
• Conductor: 54.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 54.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 54.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
54.1-b1	\( \bigl[a\) , \( a\) , \( a\) , \( -49815 a - 217148\) , \( 10424254 a + 45438265\bigr] \)
54.1-b2	\( \bigl[1\) , \( a\) , \( a\) , \( -270341 a + 1178394\) , \( 385206082 a - 1679074385\bigr] \)