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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 546.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
546.d1 | 546d3 | \([1, 0, 1, -26057, -1621108]\) | \(-1956469094246217097/36641439744\) | \(-36641439744\) | \([]\) | \(1944\) | \(1.1515\) | |
546.d2 | 546d2 | \([1, 0, 1, -122, -4948]\) | \(-198461344537/10417365504\) | \(-10417365504\) | \([3]\) | \(648\) | \(0.60215\) | |
546.d3 | 546d1 | \([1, 0, 1, 13, 182]\) | \(270840023/14329224\) | \(-14329224\) | \([3]\) | \(216\) | \(0.052847\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 546.d have rank \(0\).
Complex multiplication
The elliptic curves in class 546.d do not have complex multiplication.Modular form 546.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.