Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-147.1-c
Conductor 147.1
Rank not recorded

Related objects

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

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

Elliptic curves in class 147.1-c over \(\Q(\sqrt{57}) \)

Isogeny class 147.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
147.1-c1 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 410971 a - 1756865\) , \( -781852853 a + 3342356220\bigr] \)
147.1-c2 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 11828 a + 38741\) , \( 283917 a + 929805\bigr] \)
147.1-c3 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -48572 a - 159064\) , \( 2493022 a + 8164441\bigr] \)
147.1-c4 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -471372 a - 1543699\) , \( -339559003 a - 1112027625\bigr] \)
147.1-c5 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -592172 a - 1939309\) , \( 482038087 a + 1578634831\bigr] \)
147.1-c6 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 9470971 a - 40487615\) , \( -30838100363 a + 131830326198\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph