Properties

Label 97461.i
Number of curves $2$
Conductor $97461$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97461.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97461.i1 97461y2 [1, -1, 1, -144437, -7035640] [2] 1658880  
97461.i2 97461y1 [1, -1, 1, -115772, -15119170] [2] 829440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97461.i have rank \(1\).

Complex multiplication

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

Modular form 97461.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 4q^{5} + 3q^{8} + 4q^{10} - 6q^{11} + q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.