Elliptic curve isogeny class 225.2-e over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-225.2-e
• Conductor: 225.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.2-e over \(\Q(\sqrt{14}) \)

Isogeny class 225.2-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
225.2-e1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -6 a + 27\) , \( 0\bigr] \)
225.2-e2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 24 a - 108\) , \( 168 a - 681\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph