Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-10.1-c
Conductor 10.1
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 10.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 10.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
10.1-c1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -24 a + 110\) , \( 250 a - 960\bigr] \)
10.1-c2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 30\) , \( 42 a - 128\bigr] \)
10.1-c3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 196 a - 730\) , \( 2746 a - 10608\bigr] \)
10.1-c4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 176 a - 890\) , \( 2490 a - 8960\bigr] \)

Rank

Rank not yet determined.

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