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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4620.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4620.m1 | 4620l2 | \([0, 1, 0, -540, -540]\) | \(68150496976/39220335\) | \(10040405760\) | \([2]\) | \(3456\) | \(0.60875\) | |
| 4620.m2 | 4620l1 | \([0, 1, 0, 135, 0]\) | \(16880451584/9823275\) | \(-157172400\) | \([2]\) | \(1728\) | \(0.26218\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4620.m have rank \(1\).
Complex multiplication
The elliptic curves in class 4620.m do not have complex multiplication.Modular form 4620.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
