Elliptic curve isogeny class with Cremona label 2576k (LMFDB label 2576.b)

• Label: 2576k
• Number of curves: $2$
• Conductor: $2576$
• CM: no
• Rank: $2$

Elliptic curves in class 2576k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2576.b2	2576k1	\([0, 1, 0, -64, -204]\)	\(7189057/644\)	\(2637824\)	\([2]\)	\(576\)	\(-0.028115\)	\(\Gamma_0(N)\)-optimal
2576.b1	2576k2	\([0, 1, 0, -224, 1012]\)	\(304821217/51842\)	\(212344832\)	\([2]\)	\(1152\)	\(0.31846\)

Rank

The elliptic curves in class 2576k have rank \(2\).

Complex multiplication

The elliptic curves in class 2576k do not have complex multiplication.

Modular form 2576.2.a.k

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.