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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1620.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1620.f1 | 1620d2 | \([0, 0, 0, -60912, -5786316]\) | \(183711891456/125\) | \(17006112000\) | \([]\) | \(3888\) | \(1.2783\) | |
| 1620.f2 | 1620d1 | \([0, 0, 0, -912, -4316]\) | \(4045602816/1953125\) | \(40500000000\) | \([3]\) | \(1296\) | \(0.72902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1620.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1620.f do not have complex multiplication.Modular form 1620.2.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.
