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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 144150.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144150.db1 | 144150ca2 | \([1, 1, 1, -899556563, -9687830732719]\) | \(5805223604235668521/435937500000000\) | \(6045252123999023437500000000\) | \([2]\) | \(123863040\) | \(4.0761\) | |
144150.db2 | 144150ca1 | \([1, 1, 1, 53755437, -671405836719]\) | \(1238798620042199/14760960000000\) | \(-204693848985840000000000000\) | \([2]\) | \(61931520\) | \(3.7295\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144150.db have rank \(1\).
Complex multiplication
The elliptic curves in class 144150.db do not have complex multiplication.Modular form 144150.2.a.db
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.