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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 30960d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.g1 | 30960d1 | \([0, 0, 0, -2883, -47918]\) | \(3550014724/725625\) | \(541676160000\) | \([2]\) | \(36864\) | \(0.96701\) | \(\Gamma_0(N)\)-optimal |
30960.g2 | 30960d2 | \([0, 0, 0, 6117, -287318]\) | \(16954370638/33698025\) | \(-50310881740800\) | \([2]\) | \(73728\) | \(1.3136\) |
Rank
sage: E.rank()
The elliptic curves in class 30960d have rank \(2\).
Complex multiplication
The elliptic curves in class 30960d do not have complex multiplication.Modular form 30960.2.a.d
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.