Elliptic curve isogeny class 576.2-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-576.2-b
• Conductor: 576.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.2-b over \(\Q(\sqrt{7}) \)

Isogeny class 576.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
576.2-b1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( 7 a - 17\bigr] \)
576.2-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -53 a - 140\) , \( -323 a - 855\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph