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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 7920.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.be1 | 7920m1 | \([0, 0, 0, -98382, -11877401]\) | \(9028656748079104/3969405\) | \(46299139920\) | \([2]\) | \(24576\) | \(1.3879\) | \(\Gamma_0(N)\)-optimal |
7920.be2 | 7920m2 | \([0, 0, 0, -97887, -12002834]\) | \(-555816294307024/11837848275\) | \(-2209226596473600\) | \([2]\) | \(49152\) | \(1.7345\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.be have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.be do not have complex multiplication.Modular form 7920.2.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.