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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 9450.dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.dl1 | 9450dw2 | \([1, -1, 1, -3368930, -2317366303]\) | \(44548516344270315/1322306994176\) | \(125515859212800000000\) | \([3]\) | \(388800\) | \(2.6336\) | |
9450.dl2 | 9450dw1 | \([1, -1, 1, -3344555, -2353430053]\) | \(392296847395243635/10976\) | \(115762500000\) | \([]\) | \(129600\) | \(2.0842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.dl do not have complex multiplication.Modular form 9450.2.a.dl
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.