Elliptic curve isogeny class 56.1-d over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-56.1-d
• Conductor: 56.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 56.1-d over \(\Q(\sqrt{7}) \)

Isogeny class 56.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
56.1-d1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 15 a + 40\) , \( -161 a - 426\bigr] \)
56.1-d2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -705 a - 1865\) , \( 11554 a + 30569\bigr] \)
56.1-d3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -225 a - 595\) , \( -3396 a - 8985\bigr] \)
56.1-d4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -3585 a - 9485\) , \( -198626 a - 525515\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph