Elliptic curve isogeny class 700.1-d over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-700.1-d
• Conductor: 700.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 700.1-d over \(\Q(\sqrt{7}) \)

Isogeny class 700.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
700.1-d1	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -9664 a - 25569\) , \( -844396 a - 2234063\bigr] \)
700.1-d2	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 64 a - 169\) , \( 2245 a - 5943\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph