Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-7.1-a
Conductor 7.1
Rank \( 1 \)

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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 7.1-a over \(\Q(\sqrt{53}) \)

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
7.1-a1 \( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 351 a - 3081\) , \( 11878 a - 72832\bigr] \)
7.1-a2 \( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( a - 1\) , \( -a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph