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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 102850.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102850.di1 | 102850ce4 | \([1, 1, 1, -341888, 53028031]\) | \(159661140625/48275138\) | \(1336286746100281250\) | \([2]\) | \(1866240\) | \(2.1832\) | |
102850.di2 | 102850ce3 | \([1, 1, 1, -311638, 66822031]\) | \(120920208625/19652\) | \(543979949562500\) | \([2]\) | \(933120\) | \(1.8366\) | |
102850.di3 | 102850ce2 | \([1, 1, 1, -130138, -18119969]\) | \(8805624625/2312\) | \(63997641125000\) | \([2]\) | \(622080\) | \(1.6338\) | |
102850.di4 | 102850ce1 | \([1, 1, 1, -9138, -211969]\) | \(3048625/1088\) | \(30116537000000\) | \([2]\) | \(311040\) | \(1.2873\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102850.di have rank \(1\).
Complex multiplication
The elliptic curves in class 102850.di do not have complex multiplication.Modular form 102850.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.