Elliptic curve isogeny class 16.4-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-16.4-a
• Conductor: 16.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 16.4-a over \(\Q(\sqrt{57}) \)

Isogeny class 16.4-a contains 2 curves linked by isogenies of degree 19.

Curve label	Weierstrass Coefficients
16.4-a1	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 41678 a - 178170\) , \( 9007428 a - 38506016\bigr] \)
16.4-a2	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -2 a - 10\) , \( 3 a + 11\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph