Elliptic curve isogeny class 50.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-50.1-a
• Conductor: 50.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 50.1-a over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
50.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
50.1-a2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -10\) , \( 10\bigr] \)
50.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
50.1-a4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 90\) , \( -70\bigr] \)

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