Elliptic curve isogeny class 74.4-a over number field \(\Q(\sqrt{73}) \)

• Base field: \(\Q(\sqrt{73}) \)
• Label: 2.2.73.1-74.4-a
• Conductor: 74.4
• Rank: \( 0 \)

Base field \(\Q(\sqrt{73}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 18 \); class number \(1\).

Elliptic curves in class 74.4-a over \(\Q(\sqrt{73}) \)

Isogeny class 74.4-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
74.4-a1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2234 a + 10670\) , \( 161836 a - 772266\bigr] \)
74.4-a2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 266 a - 1260\) , \( -8433 a + 40258\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph