Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-120.1-f
Conductor 120.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 120.1-f over \(\Q(\sqrt{15}) \)

Isogeny class 120.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
120.1-f1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6 a + 35\) , \( 14 a + 62\bigr] \)
120.1-f2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -34 a - 120\) , \( 60 a + 240\bigr] \)
120.1-f3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -274 a - 1050\) , \( -4956 a - 19188\bigr] \)
120.1-f4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -434 a - 1670\) , \( 9340 a + 36180\bigr] \)

Rank

Rank: \( 0 \)

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