Elliptic curve isogeny class 150.1-c over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-150.1-c
• Conductor: 150.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 150.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 150.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
150.1-c1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -98 a - 368\) , \( 1318 a + 5112\bigr] \)
150.1-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -898 a - 3468\) , \( -138882 a - 537888\bigr] \)
150.1-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -26498 a - 102668\) , \( -4625282 a - 17913888\bigr] \)
150.1-c4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1698 a - 6568\) , \( 73718 a + 285512\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph