Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-24.1-b
Conductor 24.1
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 24.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 24.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
24.1-b1 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 29 a + 120\) , \( -1356 a - 5246\bigr] \)
24.1-b2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a + 88\) , \( 166 a + 642\bigr] \)
24.1-b3 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -11 a - 35\) , \( 13 a + 56\bigr] \)
24.1-b4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -51 a - 190\) , \( -382 a - 1474\bigr] \)
24.1-b5 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -131 a - 500\) , \( 1474 a + 5714\bigr] \)
24.1-b6 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -771 a - 2980\) , \( -23368 a - 90502\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph