Properties

Label 30960.k
Number of curves $2$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.k1 30960bj2 \([0, 0, 0, -73083, -7602518]\) \(14457238157881/4437600\) \(13250602598400\) \([2]\) \(92160\) \(1.4948\)  
30960.k2 30960bj1 \([0, 0, 0, -3963, -151382]\) \(-2305199161/1981440\) \(-5916548136960\) \([2]\) \(46080\) \(1.1482\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.k have rank \(0\).

Complex multiplication

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

Modular form 30960.2.a.k

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