Elliptic curve isogeny class 16.1-a over number field \(\Q(\sqrt{157}) \)

• Base field: \(\Q(\sqrt{157}) \)
• Label: 2.2.157.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{157}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 39 \); class number \(1\).

Elliptic curves in class 16.1-a over \(\Q(\sqrt{157}) \)

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 19.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -55 a - 318\) , \( -539 a - 3106\bigr] \)
16.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 55 a - 373\) , \( 539 a - 3645\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph