Properties

Base field \(\Q(\sqrt{301}) \)
Label 2.2.301.1-1.1-a
Conductor 1.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{301}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 75 \); class number \(1\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{301}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[a\) , \( -a\) , \( a\) , \( 400 a - 3665\) , \( -12979 a + 119119\bigr] \)
1.1-a2 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -402 a - 3265\) , \( 12978 a + 106140\bigr] \)
1.1-a3 \( \bigl[a\) , \( -a\) , \( a\) , \( 6955 a - 63805\) , \( -874060 a + 8019258\bigr] \)
1.1-a4 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6957 a - 56850\) , \( 874059 a + 7145198\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph