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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 336.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336.f1 | 336f2 | \([0, 1, 0, -36, 72]\) | \(20720464/63\) | \(16128\) | \([2]\) | \(48\) | \(-0.32399\) | |
336.f2 | 336f1 | \([0, 1, 0, -1, 2]\) | \(-16384/147\) | \(-2352\) | \([2]\) | \(24\) | \(-0.67056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 336.f have rank \(0\).
Complex multiplication
The elliptic curves in class 336.f do not have complex multiplication.Modular form 336.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.