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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 546.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
546.f1 | 546f2 | \([1, 0, 0, -3674496, -2711401518]\) | \(-5486773802537974663600129/2635437714\) | \(-2635437714\) | \([]\) | \(8232\) | \(2.0465\) | |
546.f2 | 546f1 | \([1, 0, 0, 714, -82908]\) | \(40251338884511/2997011332224\) | \(-2997011332224\) | \([7]\) | \(1176\) | \(1.0736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 546.f have rank \(0\).
Complex multiplication
The elliptic curves in class 546.f do not have complex multiplication.Modular form 546.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.