Properties

Label 73960.a
Number of curves $4$
Conductor $73960$
CM no
Rank $1$
Graph

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

Elliptic curves in class 73960.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73960.a1 73960b4 \([0, 0, 0, -197843, 33869982]\) \(132304644/5\) \(32365378810880\) \([2]\) \(314496\) \(1.6784\)  
73960.a2 73960b2 \([0, 0, 0, -12943, 477042]\) \(148176/25\) \(40456723513600\) \([2, 2]\) \(157248\) \(1.3318\)  
73960.a3 73960b1 \([0, 0, 0, -3698, -79507]\) \(55296/5\) \(505709043920\) \([2]\) \(78624\) \(0.98524\) \(\Gamma_0(N)\)-optimal
73960.a4 73960b3 \([0, 0, 0, 24037, 2703238]\) \(237276/625\) \(-4045672351360000\) \([2]\) \(314496\) \(1.6784\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73960.a have rank \(1\).

Complex multiplication

The elliptic curves in class 73960.a do not have complex multiplication.

Modular form 73960.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - 3 q^{9} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.