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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 18928.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18928.be1 | 18928bc1 | \([0, -1, 0, -1837424, -958176064]\) | \(-1214950633/196\) | \(-110675002992246784\) | \([]\) | \(449280\) | \(2.2799\) | \(\Gamma_0(N)\)-optimal |
| 18928.be2 | 18928bc2 | \([0, -1, 0, 447456, -3135209728]\) | \(17546087/7529536\) | \(-4251690914950152454144\) | \([]\) | \(1347840\) | \(2.8292\) |
Rank
sage: E.rank()
The elliptic curves in class 18928.be have rank \(1\).
Complex multiplication
The elliptic curves in class 18928.be do not have complex multiplication.Modular form 18928.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
