Properties

Label 120.a
Number of curves $4$
Conductor $120$
CM no
Rank $0$
Graph

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

Elliptic curves in class 120.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
120.a1 120b3 \([0, 1, 0, -216, -1296]\) \(546718898/405\) \(829440\) \([2]\) \(32\) \(0.069403\)  
120.a2 120b4 \([0, 1, 0, -136, 560]\) \(136835858/1875\) \(3840000\) \([2]\) \(32\) \(0.069403\)  
120.a3 120b2 \([0, 1, 0, -16, -16]\) \(470596/225\) \(230400\) \([2, 2]\) \(16\) \(-0.27717\)  
120.a4 120b1 \([0, 1, 0, 4, 0]\) \(21296/15\) \(-3840\) \([2]\) \(8\) \(-0.62374\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 120.a have rank \(0\).

Complex multiplication

The elliptic curves in class 120.a do not have complex multiplication.

Modular form 120.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4 q^{7} + q^{9} - 6 q^{13} - q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.