Elliptic curve isogeny class 4.1-d over number field \(\Q(\sqrt{-2491}) \)

• Base field: \(\Q(\sqrt{-2491}) \)
• Label: 2.0.2491.1-4.1-d
• Conductor: 4.1
• Rank bounds: 0...1

Base field \(\Q(\sqrt{-2491}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 623 \); class number \(12\).

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 4.1-d over \(\Q(\sqrt{-2491}) \)

Isogeny class 4.1-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-d1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -226 a + 7691\) , \( 6344 a - 78338\bigr] \)
4.1-d2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -181 a + 7736\) , \( 4505 a - 106427\bigr] \)