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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 473200be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
473200.be2 | 473200be1 | \([0, 1, 0, 282, 5383]\) | \(1280/7\) | \(-13515065200\) | \([]\) | \(311040\) | \(0.62599\) | \(\Gamma_0(N)\)-optimal* |
473200.be1 | 473200be2 | \([0, 1, 0, -16618, 819963]\) | \(-262885120/343\) | \(-662238194800\) | \([]\) | \(933120\) | \(1.1753\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 473200be have rank \(0\).
Complex multiplication
The elliptic curves in class 473200be do not have complex multiplication.Modular form 473200.2.a.be
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.