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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 190575dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.de1 | 190575dj1 | \([1, -1, 0, -490617, 128153416]\) | \(5177717/189\) | \(476733293244140625\) | \([2]\) | \(2073600\) | \(2.1618\) | \(\Gamma_0(N)\)-optimal |
| 190575.de2 | 190575dj2 | \([1, -1, 0, 190008, 455534041]\) | \(300763/35721\) | \(-90102592423142578125\) | \([2]\) | \(4147200\) | \(2.5083\) |
Rank
sage: E.rank()
The elliptic curves in class 190575dj have rank \(0\).
Complex multiplication
The elliptic curves in class 190575dj do not have complex multiplication.Modular form 190575.2.a.dj
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.
