Properties

Label 30960.g
Number of curves $2$
Conductor $30960$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.g1 30960d1 \([0, 0, 0, -2883, -47918]\) \(3550014724/725625\) \(541676160000\) \([2]\) \(36864\) \(0.96701\) \(\Gamma_0(N)\)-optimal
30960.g2 30960d2 \([0, 0, 0, 6117, -287318]\) \(16954370638/33698025\) \(-50310881740800\) \([2]\) \(73728\) \(1.3136\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30960.g have rank \(2\).

Complex multiplication

The elliptic curves in class 30960.g do not have complex multiplication.

Modular form 30960.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.