Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-135.1-f
Conductor 135.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 135.1-f over \(\Q(\sqrt{10}) \)

Isogeny class 135.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
135.1-f1 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 15\) , \( -8 a + 30\bigr] \)
135.1-f2 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -13 a + 5\) , \( -48 a + 178\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph