Properties

Label 273600v
Number of curves $4$
Conductor $273600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 273600v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.v4 273600v1 \([0, 0, 0, -11775, 177500]\) \(247673152/124659\) \(90876411000000\) \([2]\) \(786432\) \(1.3710\) \(\Gamma_0(N)\)-optimal
273600.v2 273600v2 \([0, 0, 0, -102900, -12580000]\) \(2582630848/29241\) \(1364268096000000\) \([2, 2]\) \(1572864\) \(1.7176\)  
273600.v3 273600v3 \([0, 0, 0, -21900, -31858000]\) \(-3112136/1172889\) \(-437778473472000000\) \([2]\) \(3145728\) \(2.0642\)  
273600.v1 273600v4 \([0, 0, 0, -1641900, -809782000]\) \(1311494070536/171\) \(63825408000000\) \([2]\) \(3145728\) \(2.0642\)  

Rank

sage: E.rank()
 

The elliptic curves in class 273600v have rank \(0\).

Complex multiplication

The elliptic curves in class 273600v do not have complex multiplication.

Modular form 273600.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.