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

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-56.1-b
• 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-b over \(\Q(\sqrt{14}) \)

Isogeny class 56.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
56.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -8820 a - 33003\) , \( 912600 a + 3414635\bigr] \)
56.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( -30 a + 112\) , \( -944 a + 3532\bigr] \)
56.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( 1770 a - 6623\) , \( 64686 a - 242033\bigr] \)
56.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -570 a - 2133\) , \( 12630 a + 47257\bigr] \)
56.1-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( 8970 a - 33563\) , \( -881050 a + 3296587\bigr] \)
56.1-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( 8820 a - 33003\) , \( -912600 a + 3414635\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph