Elliptic curve isogeny class 100.1-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-100.1-a
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-a over \(\Q(\sqrt{15}) \)

Isogeny class 100.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 5\) , \( -5 a\bigr] \)
100.1-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 5\) , \( 135 a + 525\bigr] \)
100.1-a3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 2\) , \( -2 a - 4\bigr] \)
100.1-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -200 a - 770\) , \( 3240 a + 12550\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph