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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 392784.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.h1 | 392784h2 | \([0, -1, 0, -5616984, -5122050576]\) | \(40671029123395273/37482816\) | \(18062605597016064\) | \([2]\) | \(10616832\) | \(2.4166\) | |
392784.h2 | 392784h1 | \([0, -1, 0, -348504, -81168912]\) | \(-9714044119753/301658112\) | \(-145366119295746048\) | \([2]\) | \(5308416\) | \(2.0700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 392784.h have rank \(1\).
Complex multiplication
The elliptic curves in class 392784.h do not have complex multiplication.Modular form 392784.2.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.