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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 303450.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.n1 | 303450n2 | \([1, 1, 0, -6433290, 2737905300]\) | \(9759322356711101/4572363442752\) | \(13795717261562993736000\) | \([2]\) | \(26542080\) | \(2.9426\) | |
303450.n2 | 303450n1 | \([1, 1, 0, 1427510, 324639700]\) | \(106624540661059/76738572288\) | \(-231535322945385984000\) | \([2]\) | \(13271040\) | \(2.5960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.n have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.n do not have complex multiplication.Modular form 303450.2.a.n
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.