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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 97020.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.e1 | 97020bl2 | \([0, 0, 0, -1050168, -1138058908]\) | \(-5833703071744/22107421875\) | \(-485393361799500000000\) | \([]\) | \(2985984\) | \(2.6549\) | |
97020.e2 | 97020bl1 | \([0, 0, 0, 114072, 37124948]\) | \(7476617216/31444875\) | \(-690407668244448000\) | \([]\) | \(995328\) | \(2.1056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.e have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.e do not have complex multiplication.Modular form 97020.2.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.