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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-360.1-d
• Conductor: 360.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
360.1-d1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 3 a + 45\) , \( -1010 a - 3160\bigr] \)
360.1-d2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 33 a + 25\) , \( 36 a + 272\bigr] \)
360.1-d3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -7 a - 25\) , \( 14 a + 42\bigr] \)
360.1-d4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -47 a - 155\) , \( -280 a - 900\bigr] \)
360.1-d5	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -7 a - 20\) , \( 17 a + 55\bigr] \)
360.1-d6	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -737 a - 2435\) , \( -19486 a - 62208\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph