Elliptic curve isogeny class with LMFDB label 20449.a (Cremona label 20449g)

• Label: 20449.a
• Number of curves: $3$
• Conductor: $20449$
• CM: no
• Rank: $2$

Elliptic curves in class 20449.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20449.a1	20449g3	\([0, -1, 1, -159917996, 778437705528]\)	\(-52893159101157376/11\)	\(-94060852367339\)	\([]\)	\(1296000\)	\(2.9781\)
20449.a2	20449g2	\([0, -1, 1, -211306, 67787488]\)	\(-122023936/161051\)	\(-1377144939510210299\)	\([]\)	\(259200\)	\(2.1734\)
20449.a3	20449g1	\([0, -1, 1, -6816, -512172]\)	\(-4096/11\)	\(-94060852367339\)	\([]\)	\(51840\)	\(1.3687\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 20449.a have rank \(2\).

Complex multiplication

The elliptic curves in class 20449.a do not have complex multiplication.

Modular form 20449.2.a.a

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.