Elliptic curve isogeny class 216.2-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-216.2-c
• Conductor: 216.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 216.2-c over \(\Q(\sqrt{10}) \)

Isogeny class 216.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
216.2-c1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 4 a + 28\) , \( 12 a + 50\bigr] \)
216.2-c2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -36 a - 102\) , \( 116 a + 370\bigr] \)
216.2-c3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -226 a - 742\) , \( -3292 a - 10598\bigr] \)
216.2-c4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -486 a - 1542\) , \( 10340 a + 32698\bigr] \)