Properties

Label 57330.d
Number of curves $2$
Conductor $57330$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 57330.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57330.d1 57330bs2 \([1, -1, 0, -39678795, 96212301471]\) \(27629784261491295969847/311852531250\) \(77977789881468750\) \([2]\) \(4055040\) \(2.8094\)  
57330.d2 57330bs1 \([1, -1, 0, -2477925, 1506326625]\) \(-6729249553378150807/22664098606500\) \(-5667089864259505500\) \([2]\) \(2027520\) \(2.4628\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 57330.d have rank \(0\).

Complex multiplication

The elliptic curves in class 57330.d do not have complex multiplication.

Modular form 57330.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4 q^{11} + q^{13} + q^{16} - 6 q^{17} + O(q^{20})\) Copy content 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.