Properties

Label 97461.v
Number of curves $4$
Conductor $97461$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.v1 97461k4 \([1, -1, 0, -10915641, -13878310608]\) \(1677087406638588673/4641\) \(398040567561\) \([2]\) \(1966080\) \(2.3442\)  
97461.v2 97461k2 \([1, -1, 0, -682236, -216714933]\) \(409460675852593/21538881\) \(1847306274050601\) \([2, 2]\) \(983040\) \(1.9976\)  
97461.v3 97461k3 \([1, -1, 0, -644751, -241612470]\) \(-345608484635233/94427721297\) \(-8098699370512778937\) \([2]\) \(1966080\) \(2.3442\)  
97461.v4 97461k1 \([1, -1, 0, -44991, -2982960]\) \(117433042273/22801233\) \(1955573308427193\) \([2]\) \(491520\) \(1.6511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97461.v have rank \(0\).

Complex multiplication

The elliptic curves in class 97461.v do not have complex multiplication.

Modular form 97461.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2q^{5} - 3q^{8} + 2q^{10} - 4q^{11} - q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.