Properties

Label 980.h
Number of curves $4$
Conductor $980$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 980.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
980.h1 980g3 \([0, -1, 0, -2025, 35750]\) \(488095744/125\) \(235298000\) \([2]\) \(540\) \(0.59231\)  
980.h2 980g4 \([0, -1, 0, -1780, 44472]\) \(-20720464/15625\) \(-470596000000\) \([2]\) \(1080\) \(0.93888\)  
980.h3 980g1 \([0, -1, 0, -65, -118]\) \(16384/5\) \(9411920\) \([2]\) \(180\) \(0.043005\) \(\Gamma_0(N)\)-optimal
980.h4 980g2 \([0, -1, 0, 180, -1000]\) \(21296/25\) \(-752953600\) \([2]\) \(360\) \(0.38958\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 980.2.a.h

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{5} + q^{9} - 2q^{13} + 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.