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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 8190d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8190.m1 | 8190d1 | \([1, -1, 0, -1029, -2047]\) | \(4465226119563/2499087500\) | \(67475362500\) | \([2]\) | \(7680\) | \(0.76814\) | \(\Gamma_0(N)\)-optimal |
8190.m2 | 8190d2 | \([1, -1, 0, 4041, -19285]\) | \(270250212973077/161738281250\) | \(-4366933593750\) | \([2]\) | \(15360\) | \(1.1147\) |
Rank
sage: E.rank()
The elliptic curves in class 8190d have rank \(1\).
Complex multiplication
The elliptic curves in class 8190d do not have complex multiplication.Modular form 8190.2.a.d
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 Cremona 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 Cremona labels.