Elliptic curve isogeny class 225.1-m over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-225.1-m
• Conductor: 225.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.1-m over \(\Q(\sqrt{10}) \)

Isogeny class 225.1-m contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
225.1-m1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 597 a - 1895\) , \( -14458 a + 45716\bigr] \)
225.1-m2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3 a + 5\) , \( 57 a - 184\bigr] \)
225.1-m3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 110 a - 348\) , \( 1120 a - 3542\bigr] \)
225.1-m4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 9710 a - 30748\) , \( -923880 a + 2921658\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph