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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-225.1-e
• Conductor: 225.1
• Rank: \( 1 \)

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

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

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

Isogeny class 225.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
225.1-e1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -184 a - 573\) , \( 2936 a + 9288\bigr] \)
225.1-e2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 30 a + 95\) , \( -95 a - 300\bigr] \)
225.1-e3	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -9 a - 23\) , \( -4 a - 12\bigr] \)
225.1-e4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -3070 a - 9705\) , \( 167885 a + 530900\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph