Elliptic curve isogeny class 2.1-d over number field \(\Q(\sqrt{123}) \)

• Base field: \(\Q(\sqrt{123}) \)
• Label: 2.2.492.1-2.1-d
• Conductor: 2.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{123}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 123 \); class number \(2\).

Elliptic curves in class 2.1-d over \(\Q(\sqrt{123}) \)

Isogeny class 2.1-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2.1-d1	\( \bigl[a\) , \( 0\) , \( 1\) , \( -980 a - 10548\) , \( -65571 a - 726141\bigr] \)
2.1-d2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -24785 a - 274563\) , \( 6814515 a + 75577659\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph