Properties

Label 30960.l
Number of curves $4$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.l1 30960c4 \([0, 0, 0, -71643, -235942]\) \(54477543627364/31494140625\) \(23510250000000000\) \([2]\) \(147456\) \(1.8308\)  
30960.l2 30960c2 \([0, 0, 0, -48423, 4087622]\) \(67283921459536/260015625\) \(48525156000000\) \([2, 2]\) \(73728\) \(1.4843\)  
30960.l3 30960c1 \([0, 0, 0, -48378, 4095623]\) \(1073544204384256/16125\) \(188082000\) \([2]\) \(36864\) \(1.1377\) \(\Gamma_0(N)\)-optimal
30960.l4 30960c3 \([0, 0, 0, -25923, 7899122]\) \(-2580786074884/34615360125\) \(-25840227871872000\) \([2]\) \(147456\) \(1.8308\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.