Elliptic curve isogeny class 121.1-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-121.1-b
• Conductor: 121.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 121.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 121.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
121.1-b1	\( \bigl[1\) , \( a\) , \( 1\) , \( 23 a - 92\) , \( -43 a + 187\bigr] \)
121.1-b2	\( \bigl[1\) , \( a\) , \( 1\) , \( 223 a - 947\) , \( 3267 a - 13963\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph