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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 227850.hh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.hh1 | 227850y2 | \([1, 0, 0, -2465338, 521842292]\) | \(901456690969801/457629750000\) | \(841245038402343750000\) | \([2]\) | \(16588800\) | \(2.7076\) | |
227850.hh2 | 227850y1 | \([1, 0, 0, 572662, 63104292]\) | \(11298232190519/7472736000\) | \(-13736873713500000000\) | \([2]\) | \(8294400\) | \(2.3610\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227850.hh have rank \(1\).
Complex multiplication
The elliptic curves in class 227850.hh do not have complex multiplication.Modular form 227850.2.a.hh
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.