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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5070e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.e2 | 5070e1 | \([1, 1, 0, 673, -18351]\) | \(6967871/35100\) | \(-169420995900\) | \([2]\) | \(8064\) | \(0.83686\) | \(\Gamma_0(N)\)-optimal |
5070.e1 | 5070e2 | \([1, 1, 0, -7777, -239741]\) | \(10779215329/1232010\) | \(5946676956090\) | \([2]\) | \(16128\) | \(1.1834\) |
Rank
sage: E.rank()
The elliptic curves in class 5070e have rank \(0\).
Complex multiplication
The elliptic curves in class 5070e do not have complex multiplication.Modular form 5070.2.a.e
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.