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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 19110.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19110.di1 | 19110dh2 | \([1, 0, 0, -4408755, -3563418573]\) | \(27629784261491295969847/311852531250\) | \(106965418218750\) | \([2]\) | \(506880\) | \(2.2601\) | |
19110.di2 | 19110dh1 | \([1, 0, 0, -275325, -55789875]\) | \(-6729249553378150807/22664098606500\) | \(-7773785822029500\) | \([2]\) | \(253440\) | \(1.9135\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19110.di have rank \(0\).
Complex multiplication
The elliptic curves in class 19110.di do not have complex multiplication.Modular form 19110.2.a.di
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.