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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-225.1-l
• 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-l over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
225.1-l1	\( \bigl[0\) , \( a\) , \( 0\) , \( -30 a + 95\) , \( 95 a - 300\bigr] \)
225.1-l2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 183 a - 573\) , \( -2936 a + 9288\bigr] \)
225.1-l3	\( \bigl[0\) , \( a\) , \( 0\) , \( 3070 a - 9705\) , \( -167885 a + 530900\bigr] \)
225.1-l4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8 a - 23\) , \( 4 a - 12\bigr] \)

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