Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-64.1-b
Conductor 64.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 64.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 64.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
64.1-b1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a + 31\) , \( 0\bigr] \)
64.1-b2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -32 a - 124\) , \( 0\bigr] \)
64.1-b3 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -19 a - 71\) , \( 49 a + 189\bigr] \)
64.1-b4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -20 a - 79\) , \( -172 a - 669\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph