Properties

Label 154560.ec
Number of curves $4$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 154560.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.ec1 154560gp3 \([0, -1, 0, -274785, 55533537]\) \(8753151307882969/65205\) \(17093099520\) \([2]\) \(720896\) \(1.5581\)  
154560.ec2 154560gp2 \([0, -1, 0, -17185, 870817]\) \(2141202151369/5832225\) \(1528882790400\) \([2, 2]\) \(360448\) \(1.2115\)  
154560.ec3 154560gp4 \([0, -1, 0, -10465, 1552225]\) \(-483551781049/3672913125\) \(-962832138240000\) \([2]\) \(720896\) \(1.5581\)  
154560.ec4 154560gp1 \([0, -1, 0, -1505, 2145]\) \(1439069689/828345\) \(217145671680\) \([2]\) \(180224\) \(0.86491\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154560.ec have rank \(0\).

Complex multiplication

The elliptic curves in class 154560.ec do not have complex multiplication.

Modular form 154560.2.a.ec

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + 4 q^{11} - 2 q^{13} - q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.