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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-18.3-b
• 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-b over \(\Q(\sqrt{10}) \)

Isogeny class 18.3-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
18.3-b1	\( \bigl[a\) , \( a\) , \( a\) , \( -24882 a - 78689\) , \( -3847743 a - 12167634\bigr] \)
18.3-b2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -6 a - 15\) , \( 7 a + 20\bigr] \)
18.3-b3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 24 a + 60\) , \( -746 a - 2308\bigr] \)
18.3-b4	\( \bigl[a\) , \( a\) , \( a\) , \( 258 a + 811\) , \( 1365 a + 4314\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph