Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-20.1-a
• Conductor: 20.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 20.1-a over \(\Q(\sqrt{15}) \)

Isogeny class 20.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -71 a - 272\) , \( -1174 a - 4546\bigr] \)
20.1-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 9 a + 38\) , \( 40 a + 156\bigr] \)
20.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -42 a - 160\) , \( 274 a + 1062\bigr] \)
20.1-a4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1322 a - 5120\) , \( -49390 a - 191290\bigr] \)

Rank

Rank: \( 0 \)

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