Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-36.1-e
Conductor 36.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{53}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).

Elliptic curves in class 36.1-e over \(\Q(\sqrt{53}) \)

Isogeny class 36.1-e contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
36.1-e1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -21 a - 62\) , \( 68 a + 215\bigr] \)
36.1-e2 \( \bigl[a\) , \( 1\) , \( 0\) , \( 154 a + 488\) , \( -2384 a - 7484\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph