Elliptic curve isogeny class 400.1-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-400.1-c
• Conductor: 400.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 400.1-c over \(\Q(\sqrt{10}) \)

Isogeny class 400.1-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
400.1-c1	\( \bigl[a\) , \( 0\) , \( a\) , \( -505\) , \( 3910\bigr] \)
400.1-c2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -48\) , \( -172\bigr] \)
400.1-c3	\( \bigl[a\) , \( 0\) , \( a\) , \( -5\) , \( 10\bigr] \)
400.1-c4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 352\) , \( 1268\bigr] \)

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