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SageMath
E = EllipticCurve("nd1")
E.isogeny_class()
Elliptic curves in class 435600.nd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.nd1 | 435600nd2 | \([0, 0, 0, -98175, 11844250]\) | \(-296587984/125\) | \(-44104500000000\) | \([]\) | \(1244160\) | \(1.5793\) | \(\Gamma_0(N)\)-optimal* |
435600.nd2 | 435600nd1 | \([0, 0, 0, 825, 63250]\) | \(176/5\) | \(-1764180000000\) | \([]\) | \(414720\) | \(1.0300\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435600.nd have rank \(0\).
Complex multiplication
The elliptic curves in class 435600.nd do not have complex multiplication.Modular form 435600.2.a.nd
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.