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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5220.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5220.f1 | 5220a2 | \([0, 0, 0, -1593, -30483]\) | \(-1419579648/453125\) | \(-142701750000\) | \([]\) | \(3456\) | \(0.85326\) | |
| 5220.f2 | 5220a1 | \([0, 0, 0, 147, 373]\) | \(813189888/609725\) | \(-263401200\) | \([3]\) | \(1152\) | \(0.30396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5220.f have rank \(1\).
Complex multiplication
The elliptic curves in class 5220.f do not have complex multiplication.Modular form 5220.2.a.f
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.
