Elliptic curve isogeny class 360.1-i over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-360.1-i
• Conductor: 360.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 360.1-i over \(\Q(\sqrt{10}) \)

Isogeny class 360.1-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
360.1-i1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1316 a - 3920\) , \( -46864 a - 131320\bigr] \)
360.1-i2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 20\) , \( -40 a - 40\bigr] \)
360.1-i3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1204 a - 4720\) , \( -47760 a + 154920\bigr] \)
360.1-i4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 520\) , \( -1440 a + 360\bigr] \)
360.1-i5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1196 a - 4320\) , \( -44720 a - 136600\bigr] \)
360.1-i6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -20276 a - 65520\) , \( -2831696 a - 8968120\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph