Elliptic curve isogeny class 100.1-d over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-100.1-d
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-d over \(\Q(\sqrt{10}) \)

Isogeny class 100.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-d1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -540 a - 1705\) , \( 1755 a + 5550\bigr] \)
100.1-d2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a - 130\) , \( -190 a - 600\bigr] \)
100.1-d3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -390 a - 1230\) , \( 7850 a + 24825\bigr] \)
100.1-d4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -41 a - 128\) , \( -224 a - 708\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph