Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 980a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
980.g1 980a1 \([0, 1, 0, -996, 11780]\) \(-177953104/125\) \(-76832000\) \([3]\) \(432\) \(0.44939\) \(\Gamma_0(N)\)-optimal
980.g2 980a2 \([0, 1, 0, 964, 51764]\) \(161017136/1953125\) \(-1200500000000\) \([]\) \(1296\) \(0.99869\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 980.2.a.a

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 Cremona 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 Cremona labels.