Elliptic curve isogeny class 18.3-d over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-18.3-d
• Conductor: 18.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 18.3-d over \(\Q(\sqrt{10}) \)

Isogeny class 18.3-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
18.3-d1	\( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 39\) , \( 21 a + 66\bigr] \)
18.3-d2	\( \bigl[a\) , \( a\) , \( a\) , \( 70 a + 221\) , \( 165 a + 526\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph