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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 38640.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.ce1 | 38640cm1 | \([0, 1, 0, -60398616, 180563933844]\) | \(5949010462538271898545049/3314625947988102720\) | \(13576707882959268741120\) | \([2]\) | \(5091840\) | \(3.1943\) | \(\Gamma_0(N)\)-optimal |
38640.ce2 | 38640cm2 | \([0, 1, 0, -49642136, 246922810260]\) | \(-3303050039017428591035929/4519896503737558217400\) | \(-18513496079309038458470400\) | \([2]\) | \(10183680\) | \(3.5409\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.ce do not have complex multiplication.Modular form 38640.2.a.ce
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.