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

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

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

Curve label	Weierstrass Coefficients
360.1-h1	\( \bigl[a\) , \( 0\) , \( a\) , \( 13 a + 17\) , \( 259 a + 837\bigr] \)
360.1-h2	\( \bigl[a\) , \( 0\) , \( a\) , \( 123 a + 377\) , \( -1383 a - 4393\bigr] \)
360.1-h3	\( \bigl[a\) , \( 0\) , \( a\) , \( -47 a - 153\) , \( -267 a - 847\bigr] \)
360.1-h4	\( \bigl[a\) , \( 0\) , \( a\) , \( -17 a - 58\) , \( 52 a + 162\bigr] \)
360.1-h5	\( \bigl[a\) , \( 0\) , \( a\) , \( -697 a - 2203\) , \( -18367 a - 58077\bigr] \)
360.1-h6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -272 a - 861\) , \( 4256 a + 13459\bigr] \)

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