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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 60984.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60984.be1 | 60984bj1 | \([0, 0, 0, -539055, 147844818]\) | \(1458000/49\) | \(582185660338098432\) | \([2]\) | \(608256\) | \(2.1813\) | \(\Gamma_0(N)\)-optimal |
60984.be2 | 60984bj2 | \([0, 0, 0, 179685, 513108486]\) | \(13500/2401\) | \(-114108389426267292672\) | \([2]\) | \(1216512\) | \(2.5279\) |
Rank
sage: E.rank()
The elliptic curves in class 60984.be have rank \(0\).
Complex multiplication
The elliptic curves in class 60984.be do not have complex multiplication.Modular form 60984.2.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.