Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-50.1-b
Conductor 50.1
Rank not recorded

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

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

Elliptic curves in class 50.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 50.1-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
50.1-b1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -4016 a - 15563\) , \( -282098 a - 1092579\bigr] \)
50.1-b2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
50.1-b3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -16 a - 63\) , \( -898 a - 3479\bigr] \)
50.1-b4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph