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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 17640.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17640.be1 | 17640f1 | \([0, 0, 0, -1323, 8918]\) | \(78732/35\) | \(113846584320\) | \([2]\) | \(18432\) | \(0.81710\) | \(\Gamma_0(N)\)-optimal |
17640.be2 | 17640f2 | \([0, 0, 0, 4557, 66542]\) | \(1608714/1225\) | \(-7969260902400\) | \([2]\) | \(36864\) | \(1.1637\) |
Rank
sage: E.rank()
The elliptic curves in class 17640.be have rank \(0\).
Complex multiplication
The elliptic curves in class 17640.be do not have complex multiplication.Modular form 17640.2.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 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.