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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 190575.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.e1 | 190575i2 | \([0, 0, 1, -23679170625, -1402483768477344]\) | \(116423188793017446400/91315917\) | \(1151675604153931376953125\) | \([]\) | \(253440000\) | \(4.3570\) | |
| 190575.e2 | 190575i1 | \([0, 0, 1, -73560135, 103880222586]\) | \(1363413585016606720/644626239703677\) | \(20812853513855372425550325\) | \([]\) | \(50688000\) | \(3.5523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.e have rank \(1\).
Complex multiplication
The elliptic curves in class 190575.e do not have complex multiplication.Modular form 190575.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
