Elliptic curve isogeny class 252.1-d over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-252.1-d
• Conductor: 252.1
• Rank bounds: 0...2

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

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

Elliptic curves in class 252.1-d over \(\Q(\sqrt{14}) \)

Isogeny class 252.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
252.1-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -2\bigr] \)
252.1-d2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1087 a - 4067\) , \( -40783 a - 152596\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 2\)

Isogeny matrix

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

Isogeny graph