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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 303450j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.j1 | 303450j1 | \([1, 1, 0, -68320, 6845440]\) | \(-287137850384705/22020096\) | \(-2704618291200\) | \([]\) | \(1152000\) | \(1.4337\) | \(\Gamma_0(N)\)-optimal |
303450.j2 | 303450j2 | \([1, 1, 0, 362800, 13674000]\) | \(110072002975/65345616\) | \(-3135185658281250000\) | \([]\) | \(5760000\) | \(2.2384\) |
Rank
sage: E.rank()
The elliptic curves in class 303450j have rank \(1\).
Complex multiplication
The elliptic curves in class 303450j do not have complex multiplication.Modular form 303450.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.