Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-30.1-d
Conductor 30.1
Rank \( 1 \)

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

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

Elliptic curves in class 30.1-d over \(\Q(\sqrt{15}) \)

Isogeny class 30.1-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
30.1-d1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -434 a - 1670\) , \( 31264 a + 121092\bigr] \)
30.1-d2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 46 a + 190\) , \( -1040 a - 4020\bigr] \)
30.1-d3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -14514 a - 56230\) , \( 245024 a + 948932\bigr] \)
30.1-d4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2194 a - 8490\) , \( 93264 a + 361212\bigr] \)
30.1-d5 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -594 a - 2290\) , \( -14416 a - 55828\bigr] \)
30.1-d6 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -10674 a - 41350\) , \( 1172000 a + 4539140\bigr] \)
30.1-d7 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -9234 a - 35770\) , \( -957040 a - 3706660\bigr] \)
30.1-d8 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -170674 a - 661350\) , \( 75444000 a + 292195140\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph