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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 14652.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14652.d1 | 14652c2 | \([0, 0, 0, -1411455, -645429274]\) | \(1666315860501346000/40252707\) | \(7512121191168\) | \([2]\) | \(92160\) | \(1.9907\) | |
14652.d2 | 14652c1 | \([0, 0, 0, -88320, -10059847]\) | \(6532108386304000/31987847133\) | \(373106248959312\) | \([2]\) | \(46080\) | \(1.6441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14652.d have rank \(1\).
Complex multiplication
The elliptic curves in class 14652.d do not have complex multiplication.Modular form 14652.2.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 LMFDB 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 LMFDB labels.