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

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

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

Curve label	Weierstrass Coefficients
225.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2390 a - 7568\) , \( -120440 a + 380882\bigr] \)
225.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a + 32\) , \( 480 a - 1518\bigr] \)
225.1-a3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 27 a - 88\) , \( 167 a - 531\bigr] \)
225.1-a4	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2427 a - 7688\) , \( -113058 a + 357519\bigr] \)

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