Elliptic curve isogeny class 56.1-c over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-56.1-c
• Conductor: 56.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 56.1-c over \(\Q(\sqrt{14}) \)

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

Curve label	Weierstrass Coefficients
56.1-c1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 7 a - 33\) , \( 1856 a - 6948\bigr] \)
56.1-c2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1207 a - 4523\) , \( 47106 a - 176258\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph