Properties

Label 30960.bl
Number of curves $2$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bl1 30960x2 \([0, 0, 0, -46467, 3854466]\) \(137627865747/36980\) \(2981385584640\) \([2]\) \(73728\) \(1.3771\)  
30960.bl2 30960x1 \([0, 0, 0, -3267, 44226]\) \(47832147/17200\) \(1386690969600\) \([2]\) \(36864\) \(1.0306\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.bl have rank \(1\).

Complex multiplication

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

Modular form 30960.2.a.bl

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 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.