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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4018.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4018.f1 | 4018c2 | \([1, 1, 0, -114391, 14839637]\) | \(1407074115849193/460816384\) | \(54214586761216\) | \([]\) | \(17280\) | \(1.6089\) | |
4018.f2 | 4018c1 | \([1, 1, 0, -3896, -69152]\) | \(55611739513/15438304\) | \(1816301027296\) | \([]\) | \(5760\) | \(1.0596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4018.f have rank \(0\).
Complex multiplication
The elliptic curves in class 4018.f do not have complex multiplication.Modular form 4018.2.a.f
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.