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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4176.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4176.f1 | 4176bi1 | \([0, 0, 0, -39, 146]\) | \(-35152/29\) | \(-5412096\) | \([]\) | \(960\) | \(-0.010013\) | \(\Gamma_0(N)\)-optimal |
4176.f2 | 4176bi2 | \([0, 0, 0, 321, -2374]\) | \(19600688/24389\) | \(-4551572736\) | \([]\) | \(2880\) | \(0.53929\) |
Rank
sage: E.rank()
The elliptic curves in class 4176.f have rank \(0\).
Complex multiplication
The elliptic curves in class 4176.f do not have complex multiplication.Modular form 4176.2.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.