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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 151725.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151725.be1 | 151725r2 | \([1, 0, 0, -9038023588, -292914453060583]\) | \(216486375407331255135001/27004994294227023375\) | \(10184920517523610599666802734375\) | \([2]\) | \(278691840\) | \(4.6795\) | |
151725.be2 | 151725r1 | \([1, 0, 0, 837648287, -23693762076208]\) | \(172343644217341694999/742780064187984375\) | \(-280139141424404715976318359375\) | \([2]\) | \(139345920\) | \(4.3330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 151725.be have rank \(1\).
Complex multiplication
The elliptic curves in class 151725.be do not have complex multiplication.Modular form 151725.2.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.