Properties

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

Related objects

Learn more

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

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

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

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

Curve label Weierstrass Coefficients
100.1-d1 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -114 a - 367\) , \( 1149 a + 3759\bigr] \)
100.1-d2 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( a + 8\) , \( 9 a + 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph