Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-60.1-c
Conductor 60.1
Rank \( 0 \)

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 60.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 60.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
60.1-c1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 6305 a - 24399\) , \( 532128 a - 2060894\bigr] \)
60.1-c2 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 85 a - 309\) , \( 606 a - 2318\bigr] \)
60.1-c3 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 400 a - 1529\) , \( -8117 a + 31466\bigr] \)
60.1-c4 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 6310 a - 24419\) , \( 531217 a - 2057368\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph