Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.j2 30960r1 \([0, 0, 0, -363, -1638]\) \(47832147/17200\) \(1902182400\) \([2]\) \(12288\) \(0.48127\) \(\Gamma_0(N)\)-optimal
30960.j1 30960r2 \([0, 0, 0, -5163, -142758]\) \(137627865747/36980\) \(4089692160\) \([2]\) \(24576\) \(0.82784\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6q^{13} - 2q^{17} - 2q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.