Properties

Label 2576.d
Number of curves $2$
Conductor $2576$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2576.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2576.d1 2576e2 \([0, 1, 0, -488, -4316]\) \(12576878500/1127\) \(1154048\) \([2]\) \(640\) \(0.20324\)  
2576.d2 2576e1 \([0, 1, 0, -28, -84]\) \(-9826000/3703\) \(-947968\) \([2]\) \(320\) \(-0.14333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2576.d have rank \(0\).

Complex multiplication

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

Modular form 2576.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{7} + q^{9} - 4q^{11} + 6q^{13} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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.

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

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.