Elliptic curve isogeny class 100.1-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-100.1-c
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.1-c over \(\Q(\sqrt{57}) \)

Isogeny class 100.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
100.1-c1	\( \bigl[1\) , \( -a\) , \( 1\) , \( -a + 9\) , \( -9 a + 36\bigr] \)
100.1-c2	\( \bigl[1\) , \( -a\) , \( 1\) , \( 114 a - 481\) , \( -1149 a + 4908\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph