Elliptic curve isogeny class 625.1-h over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-625.1-h
• Conductor: 625.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 625.1-h over \(\Q(\sqrt{21}) \)

Isogeny class 625.1-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
625.1-h1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3 a - 7\) , \( -2 a + 6\bigr] \)
625.1-h2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -22 a + 18\) , \( 23 a - 19\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph