Properties

Label 980.e
Number of curves $2$
Conductor $980$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 980.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
980.e1 980f1 \([0, -1, 0, -48820, -4138168]\) \(-177953104/125\) \(-9039207968000\) \([]\) \(3024\) \(1.4223\) \(\Gamma_0(N)\)-optimal
980.e2 980f2 \([0, -1, 0, 47220, -17660600]\) \(161017136/1953125\) \(-141237624500000000\) \([]\) \(9072\) \(1.9716\)  

Rank

sage: E.rank()
 

The elliptic curves in class 980.e have rank \(0\).

Complex multiplication

The elliptic curves in class 980.e do not have complex multiplication.

Modular form 980.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2 q^{9} + 6 q^{11} - 2 q^{13} - q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.