Properties

Label 152460.n
Number of curves $2$
Conductor $152460$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 152460.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152460.n1 152460be1 \([0, 0, 0, -2445168, 3044705092]\) \(-4890195460096/9282994875\) \(-3069104777588136672000\) \([]\) \(7464960\) \(2.8128\) \(\Gamma_0(N)\)-optimal
152460.n2 152460be2 \([0, 0, 0, 21077232, -64513979948]\) \(3132137615458304/7250937873795\) \(-2397274626359092984922880\) \([]\) \(22394880\) \(3.3621\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152460.n have rank \(0\).

Complex multiplication

The elliptic curves in class 152460.n do not have complex multiplication.

Modular form 152460.2.a.n

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.