Properties

Base field \(\Q(\sqrt{301}) \)
Label 2.2.301.1-20.1-a
Conductor 20.1
Rank \( 0 \)

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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 20.1-a over \(\Q(\sqrt{301}) \)

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.1-a1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 11440 a - 104961\) , \( 2035889 a - 18678595\bigr] \)
20.1-a2 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4082737 a + 33375119\) , \( -72075964995 a - 589197645731\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph