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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)
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.