Elliptic curve isogeny class 484.1-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-484.1-a
• Conductor: 484.1
• Rank: \( 2 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 484.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 484.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
484.1-a1	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -928 a - 2455\) , \( 25483 a + 67421\bigr] \)
484.1-a2	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -32 a + 85\) , \( -174 a + 457\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph