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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 32490.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.h1 | 32490a2 | \([1, -1, 0, -473595, -116687675]\) | \(63433837731204513/4882812500000\) | \(904262695312500000\) | \([2]\) | \(512000\) | \(2.1900\) | |
32490.h2 | 32490a1 | \([1, -1, 0, -464475, -121723739]\) | \(59839327109608353/400000000\) | \(74077200000000\) | \([2]\) | \(256000\) | \(1.8435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.h have rank \(1\).
Complex multiplication
The elliptic curves in class 32490.h do not have complex multiplication.Modular form 32490.2.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.