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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 143325dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143325.dr2 | 143325dj1 | \([0, 0, 1, -1470, 20151]\) | \(163840/13\) | \(27873989325\) | \([]\) | \(103680\) | \(0.74784\) | \(\Gamma_0(N)\)-optimal |
143325.dr1 | 143325dj2 | \([0, 0, 1, -23520, -1384434]\) | \(671088640/2197\) | \(4710704195925\) | \([]\) | \(311040\) | \(1.2971\) |
Rank
sage: E.rank()
The elliptic curves in class 143325dj have rank \(0\).
Complex multiplication
The elliptic curves in class 143325dj do not have complex multiplication.Modular form 143325.2.a.dj
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.