Elliptic curve isogeny class 196.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-196.1-b
• Conductor: 196.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 196.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 196.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
196.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 280 a - 1043\) , \( 1281 a - 4795\bigr] \)
196.1-b2	\( \bigl[0\) , \( a\) , \( 0\) , \( -17080 a - 63903\) , \( -2371621 a - 8873795\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph