Properties

Label 45980c
Number of curves $2$
Conductor $45980$
CM no
Rank $0$
Graph

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

Elliptic curves in class 45980c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45980.e1 45980c1 \([0, -1, 0, -111481, -13324650]\) \(5405726654464/407253125\) \(11543580054050000\) \([2]\) \(345600\) \(1.8273\) \(\Gamma_0(N)\)-optimal
45980.e2 45980c2 \([0, -1, 0, 106924, -59364424]\) \(298091207216/3525390625\) \(-1598833802500000000\) \([2]\) \(691200\) \(2.1739\)  

Rank

sage: E.rank()
 

The elliptic curves in class 45980c have rank \(0\).

Complex multiplication

The elliptic curves in class 45980c do not have complex multiplication.

Modular form 45980.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} - 2 q^{7} + q^{9} - 6 q^{13} - 2 q^{15} - 2 q^{17} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.