Elliptic curve isogeny class 112.1-d over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-112.1-d
• Conductor: 112.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 112.1-d over \(\Q(\sqrt{14}) \)

Isogeny class 112.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
112.1-d1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 13 a - 26\) , \( -1826 a + 6853\bigr] \)
112.1-d2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1213 a - 4516\) , \( -43476 a + 162693\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph