Properties

Label 558.c
Number of curves $4$
Conductor $558$
CM no
Rank $0$
Graph

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

Elliptic curves in class 558.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
558.c1 558c3 \([1, -1, 0, -2976, -61750]\) \(3999236143617/62\) \(45198\) \([2]\) \(256\) \(0.44123\)  
558.c2 558c4 \([1, -1, 0, -276, 134]\) \(3196010817/1847042\) \(1346493618\) \([2]\) \(256\) \(0.44123\)  
558.c3 558c2 \([1, -1, 0, -186, -928]\) \(979146657/3844\) \(2802276\) \([2, 2]\) \(128\) \(0.094655\)  
558.c4 558c1 \([1, -1, 0, -6, -28]\) \(-35937/496\) \(-361584\) \([2]\) \(64\) \(-0.25192\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 558.c have rank \(0\).

Complex multiplication

The elliptic curves in class 558.c do not have complex multiplication.

Modular form 558.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{8} - 2 q^{10} + 2 q^{13} + q^{16} + 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.