Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-225.1-c
Conductor 225.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 225.1-c over \(\Q(\sqrt{13}) \)

Isogeny class 225.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
225.1-c1 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 23 a - 55\) , \( 104 a - 241\bigr] \)
225.1-c2 \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -375 a - 681\) , \( -4755 a - 7417\bigr] \)
225.1-c3 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 398 a - 930\) , \( 5879 a - 13566\bigr] \)
225.1-c4 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 373 a - 1055\) , \( 4754 a - 12171\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph