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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 54390e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54390.d2 | 54390e1 | \([1, 1, 0, 4652917, 72631007037]\) | \(276068669869428353/56630352960000000\) | \(-2285239007619126720000000\) | \([2]\) | \(7902720\) | \(3.3533\) | \(\Gamma_0(N)\)-optimal |
| 54390.d1 | 54390e2 | \([1, 1, 0, -235392203, 1350103126653]\) | \(35745187142035558575487/1169532421875000000\) | \(47194851726101953125000000\) | \([2]\) | \(15805440\) | \(3.6998\) |
Rank
sage: E.rank()
The elliptic curves in class 54390e have rank \(1\).
Complex multiplication
The elliptic curves in class 54390e do not have complex multiplication.Modular form 54390.2.a.e
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 Cremona 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 Cremona labels.
