Properties

Label 5600.c
Number of curves $2$
Conductor $5600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5600.c1 5600p2 \([0, 1, 0, -208, 588]\) \(125000/49\) \(392000000\) \([2]\) \(2304\) \(0.34752\)  
5600.c2 5600p1 \([0, 1, 0, 42, 88]\) \(8000/7\) \(-7000000\) \([2]\) \(1152\) \(0.00094497\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5600.c have rank \(0\).

Complex multiplication

The elliptic curves in class 5600.c do not have complex multiplication.

Modular form 5600.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} + 4q^{11} + 4q^{13} + 2q^{17} + 6q^{19} + O(q^{20})\)  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.