Elliptic curve isogeny class 14.2-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-14.2-a
• Conductor: 14.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 14.2-a over \(\Q(\sqrt{15}) \)

Isogeny class 14.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
14.2-a1	\( \bigl[a\) , \( 1\) , \( 1\) , \( -91 a - 343\) , \( -152 a - 585\bigr] \)
14.2-a2	\( \bigl[a\) , \( 1\) , \( 1\) , \( -5011 a - 19398\) , \( 371997 a + 1440742\bigr] \)
14.2-a3	\( \bigl[a\) , \( 1\) , \( 1\) , \( -5061 a - 19593\) , \( -393664 a - 1524653\bigr] \)