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

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-98.1-l
• 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-l over \(\Q(\sqrt{15}) \)

Isogeny class 98.1-l contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
98.1-l1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 5458 a - 21138\) , \( -429456 a + 1663276\bigr] \)
98.1-l2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 18 a - 58\) , \( 160 a - 612\bigr] \)
98.1-l3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -142 a + 562\) , \( -3184 a + 12340\bigr] \)
98.1-l4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1138 a - 4398\) , \( -32880 a + 127348\bigr] \)
98.1-l5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 338 a - 1298\) , \( 6848 a - 26516\bigr] \)
98.1-l6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 87378 a - 338578\) , \( -27618704 a + 106967340\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph