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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 19110.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19110.f1 | 19110k2 | \([1, 1, 0, -56032, 5272576]\) | \(-397052665540282969/17493884928000\) | \(-857200361472000\) | \([]\) | \(116640\) | \(1.6305\) | |
19110.f2 | 19110k1 | \([1, 1, 0, 3503, 21589]\) | \(96973777690391/59691453120\) | \(-2924881202880\) | \([]\) | \(38880\) | \(1.0812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19110.f have rank \(1\).
Complex multiplication
The elliptic curves in class 19110.f do not have complex multiplication.Modular form 19110.2.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.