Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-256.1-h
Conductor 256.1
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 256.1-h over \(\Q(\sqrt{57}) \)

Isogeny class 256.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
256.1-h1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 133 a + 436\bigr] \)
256.1-h2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -133 a + 574\bigr] \)
256.1-h3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -199 a - 650\) , \( 3294 a + 10788\bigr] \)
256.1-h4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 201 a - 850\) , \( -3094 a + 13232\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph