Elliptic curve isogeny class 120.1-c over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-120.1-c
• Conductor: 120.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 120.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 120.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
120.1-c1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -160 a - 621\) , \( -19060 a - 73821\bigr] \)
120.1-c2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 160 a + 619\) , \( 790 a + 3059\bigr] \)
120.1-c3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -40 a - 156\) , \( -40 a - 156\bigr] \)
120.1-c4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -400 a - 1551\) , \( -9472 a - 36687\bigr] \)
120.1-c5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -490 a - 1896\) , \( 12426 a + 48126\bigr] \)
120.1-c6	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -6400 a - 24801\) , \( -563572 a - 2182737\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph