Elliptic curve isogeny class 8.1-d over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-8.1-d
• Conductor: 8.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 8.1-d over \(\Q(\sqrt{15}) \)

Isogeny class 8.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
8.1-d1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -4\) , \( -2\bigr] \)
8.1-d2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 49\) , \( -36 a + 125\bigr] \)
8.1-d3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9\) , \( -2 a - 7\bigr] \)
8.1-d4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -10 a - 49\) , \( -56 a - 219\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph