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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-8.1-a
• Conductor: 8.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
8.1-a1	\( \bigl[0\) , \( a\) , \( 0\) , \( -8 a - 26\) , \( -64 a - 250\bigr] \)
8.1-a2	\( \bigl[0\) , \( a\) , \( 0\) , \( -208 a - 806\) , \( -1388 a - 5366\bigr] \)
8.1-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a - 646\) , \( -2548 a - 9870\bigr] \)
8.1-a4	\( \bigl[0\) , \( a\) , \( 0\) , \( -2688 a - 10406\) , \( -152764 a - 591654\bigr] \)

Rank

Rank: \( 1 \)

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