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 Torsion structure Modular degree Optimality
97461.v1 97461k4 [1, -1, 0, -10915641, -13878310608] [2] 1966080  
97461.v2 97461k2 [1, -1, 0, -682236, -216714933] [2, 2] 983040  
97461.v3 97461k3 [1, -1, 0, -644751, -241612470] [2] 1966080  
97461.v4 97461k1 [1, -1, 0, -44991, -2982960] [2] 491520 \(\Gamma_0(N)\)-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)
 
\( q + q^{2} - q^{4} + 2q^{5} - 3q^{8} + 2q^{10} - 4q^{11} - q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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.