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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-14.2-d
• Conductor: 14.2
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

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-d over \(\Q(\sqrt{15}) \)

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

Curve label	Weierstrass Coefficients
14.2-d1	\( \bigl[1\) , \( 1\) , \( a\) , \( -91 a - 350\) , \( -29 a - 116\bigr] \)
14.2-d2	\( \bigl[1\) , \( 1\) , \( a\) , \( -5011 a - 19405\) , \( -382018 a - 1479553\bigr] \)
14.2-d3	\( \bigl[1\) , \( 1\) , \( a\) , \( -5061 a - 19600\) , \( 383543 a + 1485452\bigr] \)