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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 39984.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39984.e1 | 39984bj2 | \([0, -1, 0, -10738072, 13436333296]\) | \(5799070911693913/54760833024\) | \(1293047009188201365504\) | \([]\) | \(2177280\) | \(2.8717\) | |
39984.e2 | 39984bj1 | \([0, -1, 0, -941992, -340873616]\) | \(3914907891433/135834624\) | \(3207412024401199104\) | \([]\) | \(725760\) | \(2.3224\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39984.e have rank \(1\).
Complex multiplication
The elliptic curves in class 39984.e do not have complex multiplication.Modular form 39984.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.