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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 7056.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.bz1 | 7056bz2 | \([0, 0, 0, -5020491, 4351903738]\) | \(-16591834777/98304\) | \(-82916138081650212864\) | \([]\) | \(241920\) | \(2.6623\) | |
| 7056.bz2 | 7056bz1 | \([0, 0, 0, 165669, 31832458]\) | \(596183/864\) | \(-728755119858253824\) | \([]\) | \(80640\) | \(2.1130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.bz do not have complex multiplication.Modular form 7056.2.a.bz
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.
