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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 88935.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88935.bc1 | 88935bh2 | \([0, -1, 1, -4988265, -4286708119]\) | \(-65860951343104/3493875\) | \(-728201743233454875\) | \([]\) | \(2488320\) | \(2.4953\) | |
| 88935.bc2 | 88935bh1 | \([0, -1, 1, -7905, -15675892]\) | \(-262144/509355\) | \(-106160981410232595\) | \([]\) | \(829440\) | \(1.9459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 88935.bc do not have complex multiplication.Modular form 88935.2.a.bc
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.
