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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-360.1-b
• 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-b over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
360.1-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 520 a - 1816\) , \( 12288 a - 40656\bigr] \)
360.1-b2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
360.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -16\) , \( -16\bigr] \)
360.1-b4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -136\) , \( 560\bigr] \)
360.1-b5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -216\) , \( -1296\bigr] \)
360.1-b6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -520 a - 1816\) , \( -12288 a - 40656\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph