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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 450800v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.v2 | 450800v1 | \([0, 1, 0, 734592, -1384620812]\) | \(16974593/330625\) | \(-853882324120000000000\) | \([2]\) | \(20643840\) | \(2.6967\) | \(\Gamma_0(N)\)-optimal* |
450800.v1 | 450800v2 | \([0, 1, 0, -15043408, -21233344812]\) | \(145780726447/8984375\) | \(23203324025000000000000\) | \([2]\) | \(41287680\) | \(3.0433\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800v have rank \(0\).
Complex multiplication
The elliptic curves in class 450800v do not have complex multiplication.Modular form 450800.2.a.v
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.