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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 45486.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45486.h1 | 45486d2 | \([1, -1, 0, -105226542, -415390106412]\) | \(25769813722208652671875/3599030964436992\) | \(17995914217718456205312\) | \([2]\) | \(7884800\) | \(3.2873\) | |
45486.h2 | 45486d1 | \([1, -1, 0, -7168302, -5251711788]\) | \(8146748259978623875/2330074250477568\) | \(11650862898054690766848\) | \([2]\) | \(3942400\) | \(2.9407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45486.h have rank \(0\).
Complex multiplication
The elliptic curves in class 45486.h do not have complex multiplication.Modular form 45486.2.a.h
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.