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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 46800.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.er1 | 46800ew1 | \([0, 0, 0, -1312740075, -18306959838950]\) | \(-134057911417971280740025/1872\) | \(-3493601280000\) | \([]\) | \(6451200\) | \(3.3865\) | \(\Gamma_0(N)\)-optimal |
| 46800.er2 | 46800ew2 | \([0, 0, 0, -1279090875, -19289874473750]\) | \(-198417696411528597145/22989483914821632\) | \(-26814934038247951564800000000\) | \([]\) | \(32256000\) | \(4.1912\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.er have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.er do not have complex multiplication.Modular form 46800.2.a.er
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
