Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-1156.1-c
Conductor 1156.1
Rank \( 1 \)

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 1156.1-c over \(\Q(\sqrt{53}) \)

Isogeny class 1156.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1156.1-c1 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 8 a + 24\) , \( 52 a + 162\bigr] \)
1156.1-c2 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -2 a - 6\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph