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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 471600fr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 471600.fr2 | 471600fr1 | \([0, 0, 0, -142275, 20637250]\) | \(6826561273/7074\) | \(330044544000000\) | \([]\) | \(3151872\) | \(1.7036\) | \(\Gamma_0(N)\)-optimal |
| 471600.fr1 | 471600fr2 | \([0, 0, 0, -520275, -122624750]\) | \(333822098953/53954184\) | \(2517286408704000000\) | \([]\) | \(9455616\) | \(2.2529\) |
Rank
sage: E.rank()
The elliptic curves in class 471600fr have rank \(1\).
Complex multiplication
The elliptic curves in class 471600fr do not have complex multiplication.Modular form 471600.2.a.fr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
