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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 424830m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.m2 | 424830m1 | \([1, 1, 0, -99838, 12080692]\) | \(190407092777/360000\) | \(208083433320000\) | \([2]\) | \(2211840\) | \(1.6373\) | \(\Gamma_0(N)\)-optimal |
424830.m1 | 424830m2 | \([1, 1, 0, -133158, 3277548]\) | \(451747330217/253125000\) | \(146308664053125000\) | \([2]\) | \(4423680\) | \(1.9839\) |
Rank
sage: E.rank()
The elliptic curves in class 424830m have rank \(2\).
Complex multiplication
The elliptic curves in class 424830m do not have complex multiplication.Modular form 424830.2.a.m
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.