Elliptic curve isogeny class 50.1-e over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-50.1-e
• Conductor: 50.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 50.1-e over \(\Q(\sqrt{15}) \)

Isogeny class 50.1-e contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
50.1-e1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -123\) , \( 427\bigr] \)
50.1-e2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 95 a - 365\) , \( 1450 a - 5615\bigr] \)
50.1-e3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( 2\bigr] \)
50.1-e4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -705 a + 2735\) , \( -10690 a + 41405\bigr] \)