Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.a1 30960br1 \([0, 0, 0, -3243, 69658]\) \(1263214441/29025\) \(86668185600\) \([2]\) \(36864\) \(0.88511\) \(\Gamma_0(N)\)-optimal
30960.a2 30960br2 \([0, 0, 0, 357, 215818]\) \(1685159/6739605\) \(-20124352696320\) \([2]\) \(73728\) \(1.2317\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.a

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