Elliptic curve isogeny class 90.1-c over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-90.1-c
• Conductor: 90.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 90.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 90.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
90.1-c1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -17\bigr] \)
90.1-c2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 735\) , \( 1290 a + 4995\bigr] \)
90.1-c3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -771 a - 2985\) , \( 3762 a + 14571\bigr] \)
90.1-c4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -123\) , \( -713\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph