Elliptic curve isogeny class 98.1-f over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-98.1-f
• Conductor: 98.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 98.1-f over \(\Q(\sqrt{15}) \)

Isogeny class 98.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
98.1-f1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 674 a - 2609\) , \( 20386 a - 78954\bigr] \)
98.1-f2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 174674 a - 676529\) , \( 78424498 a - 303736762\bigr] \)
98.1-f3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 10914 a - 42289\) , \( 1235618 a - 4785514\bigr] \)
98.1-f4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 10994 a - 42929\) , \( 1207186 a - 4673306\bigr] \)

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