Elliptic curve isogeny class 56.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-56.1-b
• Conductor: 56.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 56.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 56.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
56.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 5\) , \( 384 a + 1015\bigr] \)
56.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 484 a - 1279\) , \( -9793 a + 25911\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph