Elliptic curve isogeny class 625.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-625.1-b
• Conductor: 625.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 625.1-b over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
625.1-b1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 132 a - 311\) , \( -912 a + 2097\bigr] \)
625.1-b2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2007 a - 4686\) , \( -66537 a + 153347\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph